Physics Book - User contributions [en]

Combining Electric and Magnetic Forces

2016-04-18T02:18:29Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016 - ''Added middle and difficult examples, figures, and minor format changes'')

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces; if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See '''Figure 5'''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See '''Figure 6'''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBL

I = (vBL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T02:14:03Z

Ajacob30:

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016 - ''Added middle and difficult examples, figures, and minor format changes'')

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces; if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See '''Figure 5'''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See '''Figure 6'''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T02:13:49Z

Ajacob30:

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016 - ''Added middle and difficult examples, figures, and minor format changes)''

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces; if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See '''Figure 5'''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See '''Figure 6'''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T02:13:02Z

Ajacob30: /* Examples */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016) ''(Added middle and difficult examples, figures, and minor format changes)''

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces; if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See '''Figure 5'''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See '''Figure 6'''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T02:10:47Z

Ajacob30:

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016) ''(Added middle and difficult examples, figures, and minor format changes)''

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces; if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T02:00:53Z

Ajacob30: /* Magnetic Forces */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero; this is due to AxB = |A||B|sin(θ). If the angle between the two vectors is 0 or 180 degrees (parallel), then sin(θ) = 0. Therefore, AxB = 0.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:57:18Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0> and r = 1.4e-3 m

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:56:36Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) + 0 = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0>

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:55:41Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0>

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''-

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:54:58Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0>

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]
'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:54:14Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' At a particular instant, a proton is moving with velocity <0,5e5,0> m/s and an electron is moving with velocity <-4.2e2,0,0> m/s. The electron is located 1.4e-3 m below the proton (in the -y direction).

Determine the net force on the electron due to the proton.

'''A:''' Fnet = F(e) + F(B)

@ the electron's location, B = 0 because the velocity of the proton is parallel to r-hat.

Fnet = F(e) = q*E

E = (1/4πεo)*(q/r^2)*rhat

where rhat = <0,-1,0>

E = <0,-7.35e-4,0> N/C

Fnet = -e*E = <0,1.18e-22,0> N

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:44:07Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:43:58Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:40:33Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:40:24Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:39:54Z

Ajacob30: /* Simple */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The magnetic field is in the +z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:39:36Z

Ajacob30: /* Simple */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:39:22Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:39:09Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length L and zero resistance slides at a constant velocity, v. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:34:29Z

Ajacob30: /* Difficult */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===

===Difficult===
'''Q:''' A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:34:18Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:33:24Z

Ajacob30: /* Simple */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

'''Q:''' A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

'''A:''' |qE| = |qvB|

E = vB

B = E/v = 3.6e7/7e8

B = 0.051 T

The Magnetic Field is in the +Z direction.

===Middling===
'''Q:''' A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:30:18Z

Ajacob30: /* Applications */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
'''Q:''' A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.

===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:29:58Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
'''Q:''' A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

'''A:''' ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:29:42Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A: ''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:29:19Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV. See ''Figure 5''.

[[File:Middle_Example_A.jpg|thumb| '''Figure 5.''' Middle example diagram. ]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:

''Direction of the Magnetic Force''- Use right hand rule for v cross B. See ''Figure 6''.

[[File:Middle_Example_B.jpg|thumb| '''Figure 6.''' Middle example solution. ]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:26:06Z

Ajacob30: /* Electric and Magnetic Forces Combined */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:

::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:

[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.

[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:

''Direction of the Magnetic Force''- Use right hand rule for v cross B.

[[File:Middle_Example_B.jpg]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:25:42Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.

[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:

''Direction of the Magnetic Force''- Use right hand rule for v cross B.

[[File:Middle_Example_B.jpg]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:25:03Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.

[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:

''Direction of the Magnetic Force''

[[File:Middle_Example_B.jpg]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:24:44Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.
[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:

''Direction of the Magnetic Force''

[[File:Middle_Example_B.jpg]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:24:32Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.
[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:
''Direction of the Magnetic Force''

[[File:Middle_Example_B.jpg]]

''Current through the resistor''

ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T01:24:11Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.
[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:
''Direction of the Magnetic Force''
[[File:Middle_Example_B.jpg]]

''Current through the resistor''
ΔV round trip = 0

ΔV round trip = +motional emf - ΔV resistor = 0

motional emf = IR

I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|

q*E = q*v*B

E = v*B

|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

File:Middle Example A.jpg

2016-04-18T01:22:38Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example A.jpg"

File:Middle Example B.jpg

2016-04-18T01:22:23Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example B.jpg"

File:Middle Example B.jpg

2016-04-18T01:22:04Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example B.jpg"

File:Middle Example A.jpg

2016-04-18T01:21:48Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example A.jpg"

Combining Electric and Magnetic Forces

2016-04-18T01:16:27Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length d and zero resistance slides at a constant velocity, v, along a metal rail and moves a distance L. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.
[[File:Middle_Example_A.jpg]]

Determine the direction of the magnetic force on the diagram and the current through the resistor. Your answer should be in terms of the given variables.

A:
''Direction of the Magnetic Force''
[[File:Middle_Example_B.jpg]]

''Current through the resistor''
ΔV round trip = 0
ΔV round trip = +motional emf - ΔV resistor = 0
motional emf = IR
I = (motional emf/R)

According to Lorentz force, |F(e)| = |F(B)|
q*E = q*v*B
E = v*B
|ΔV| = E*ΔL = vBΔL

I = (vBΔL)/R

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

File:Middle Example B.jpg

2016-04-18T01:00:39Z

Ajacob30:

File:Middle Example A.jpg

2016-04-18T00:59:32Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example A.jpg"

File:Middle Example A.jpg

2016-04-18T00:57:47Z

Ajacob30: Ajacob30 uploaded a new version of "File:Middle Example A.jpg"

File:Middle Example A.jpg

2016-04-18T00:54:52Z

Ajacob30:

Combining Electric and Magnetic Forces

2016-04-18T00:53:42Z

Ajacob30: /* Middling */

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
Q: A copper bar of length L and zero resistance slides at a constant velocity, v, along a metal rail. There is a uniform magnetic field, B, directed into the page. A voltmeter is connected across a resistor, R, and reads ΔV.

Determine the magnitude of the magnetic force acting on the bar and indicate the direction of this force on the diagram. Your answer should be in terms of the given variables.

===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

Combining Electric and Magnetic Forces

2016-04-18T00:32:08Z

Ajacob30:

Claimed by Alana Kaplan (Fall, 2015); Claimed to Edit by Alexis Jacob (Spring 2016)

Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]], [[Motional Emf]], [[Inductance]] and [[Magnetic Torque]].

An easy way to conceptualize the net force principle, [[Lorentz Force]], is when a charged particle is moving through a space with present electric and magnetic forces, if the forces are not equal but opposite, the particles trajectory will change.

==The Main Idea==
===A Mathematical Model===

====Electric Forces====

[[File:ElectricForces.jpg|thumb| '''Figure 1.''' An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles. ]]

:• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See '''Figure 1''') .

:• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

::1) A (-) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)
::2) A (+) charged Particle(1) is acting on a (-) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::3) A (-) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially inward toward Particle(1)
::4) A (+) charged Particle(1) is acting on a (+) charged particle(2)
:::• Particle(2) feels force pointing radially outward from Particle(1)

The electric force formula is as follows:
::[[File:ForceE FORM.jpg]]
::Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source
:::*Note that electric forces can perform work

====Magnetic Forces====

[[File:Magnetic Force Lines.jpg|thumb| '''Figure 2.''' Magnetic Fields follow a helical pattern ]]
[[File:RightHandRule.jpg|thumb| '''Figure 3.''' Magnetic Force Right Hand Rule]]

:• The magnetic force on a charged particle is orthogonal to the magnetic field.

:• The particle must be moving with some velocity for a magnetic force to be present.

:• Particles move perpendicular to the magnetic field lines in a helical manner (See '''Figure 2''')

:• To find the magnetic force, you can use the Right Hand Rule as follows (See '''Figure 3'''):

:::1) Thumb in direction of the velocity
:::2)Fingers in the direction of the magnetic field
:::3) Your palm will face in the direction of the Magnetic Force

The magnetic force on an object is:
::[[File:ForceB.jpg]]
Note that if the velocity and magnetic field are parallel the magnetic force is zero.

====Electric and Magnetic Forces Combined====
[[File:Velocity selector.gif|thumb| '''Figure 4.''' The electric field, magnetic field, and velocity vector are all perpendicular to each other ]]
The net force acting on a particle passing through a magnetic and electric field is:
::[[File:Fnet.jpg]]
This net force calculation is known as "Lorentz Force"

When the net force is equal to zero, the velocity stays constant. The net force is equal when:
[[File:Force=0.jpg]]

As seen in '''Figure 4''' , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite. When forces are not balanced the trajectory of the the particle will change.

The Lorentz Force calculation is now a fundamental principle of electromagnetism.

==Examples==

===Simple===

Q: A proton is moving with velocity 7e8 in the +x direction. The trajectory of the proton is constant. There is an electric field in the area of 3.6e7 in the +y direction. Calculate the direction and magnitude of the magnetic field acting on the particle?

A: [[File:Solution1.jpg]]

The Magnetic Field is in the +Z direction.

===Middling===
===Difficult===

==Connectedness==

The Lorentz Force principle has been a component in many modern day inventions and critical building block for many physics principles. With known forces, we can predict the very important figure, the velocity and trajectory of a moving particle.

===Applications===

'''''Velocity Selector'''''
[[File:Velocityselector2.png|thumb| '''Figure 5.''' Illustration of a Velocity Selector ]]

The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 5''' ). Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.

'''''Electric Motor'''''

An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. Using the [[magnetic torque]] principle, electric energy is created by using the magnetic field of a magnet. The [[torque]] laws are based off the principles of the net electric and magnetic forces.
===Other related topics===

Here are other principles that use the net force of magnetic and electric forces as a building block:

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

== See also ==

[[Hall Effect]]

[[Lorentz Force]]

[[Motional Emf]]

[[Electric Motors]]

[[Motional Emf using Faraday's Law]]

[[Inductance]]

===Further reading===

Books, Articles or other print media on this topic

[http://web.mit.edu/sahughes/www/8.022/lec10.pdf | MIT Physics notes on Lorentz force]

===External links===
Great youtube videos on Lorentz Force Law:
[https://www.youtube.com/watch?v=gINzRCOOs-8 |Lorentz Force Law Video 1]
[https://www.youtube.com/watch?v=PK6sEF9SNjw | Lorentz Force Law Video 2]

==References==

Boundless. “Electric vs. Magnetic Forces.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 05 Dec. 2015 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/magnetism-21/motion-of-a-charged-particle-in-a-magnetic-field-158/electric-vs-magnetic-forces-554-11176/

Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Vol. 2. Hoboken, NJ: Wiley, 2015. 812-814. Print.

All images found on google image search:
https://en.wikipedia.org/wiki/Magnetic_field
https://en.wikipedia.org/wiki/Wien_filter
http://aplusphysics.com/wordpress/regents/em/electric-field/

[[Fields]]

John Bardeen

2015-12-03T03:08:09Z

Ajacob30: /* Bardeen-Cooper-Schrieffer Theory (BCS Theory) */

Claimed by Alexis Jacob (ajacob30) 12/2/2015

John Bardeen (May 23, 1908-Jan 30, 1991) was an American physicist who was cowinner of the Nobel Prize for physics in 1956 and 1972 [http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html]. The 1956 Nobel Prize was for the joint invention of the transistor with William B. Shockley and Walter H. Brattain. The 1972 Nobel Prize was for developing the theory of superconductivity with Leon N. Cooper and John R. Schrieffer [http://www.britannica.com/biography/John-Bardeen].

[[File:John_Bardeen.jpg]]

===University Education and Career===
Bardeen earned his bachelor's and master's in electrical engineering at the University of Wisconsin, Madison. He received his doctorate in mathermatical physics from Princeton University in 1936. He later became a staff member at eh University of Minnesota, Minneapolis from 1938 to 1941. During World War II, he served as principal physicist at the U.S. Naval Ordinance Laboratory in Washington, D.C. From 1951 to 1975, Bardeen served as a professor of electrical engineering and physics at the University of Illinois, Urbana-Champaign [http://www.britannica.com/biography/John-Bardeen].

==Scientific Contribution==
In 1945, Bardeen joined Bell Laboratories where he researched the electron-conducting properties of semiconductors with his colleagues, Brattain and Shockley. Together on Dec. 23, 1947, they began the electronic revolution with the creation of the transistor. This device allowed computers to be manufactured with smaller and more accessible parts [http://www.britannica.com/biography/John-Bardeen].
In the early 1950s, Bardeen continued research on superconductivity at near absolute temperatures. He created the BCS theory, with Cooper and Schrieffer, to explain the disappearance of electrical resistance in materials near such extreme temperatures [http://www.britannica.com/biography/John-Bardeen].

===Transistor===
A transistor is a semiconductor that amplifies, controls, and generates electrical signals. It is made up of integrated circuits called microchips. Its small size, low heat generation, and power efficiency made it the foundation of the Information Age. The three leads in a transistor are the emitter, collector, and the base which in modern appliances are known as the source, drain, and gate. The electrical signal applied at the base influences the semiconductor's ability to conduct current. The current then flows between the emitter and collector. The rate of flow of current is determined by the input signal at the gate [http://www.britannica.com/technology/transistor].

[[File:Transistor.jpg]]

===Bardeen-Cooper-Schrieffer Theory (BCS Theory)===
BCS theory is a comprehensive theory that explains the behavior of superconducting materials; they lost resistance to the flow of electric current when cooled to temperatures near zero. Superconductors form when electrons in pairs, called Cooper pairs, in a material all have correlated motion. After applying voltage and removing the voltage, the current continues flowing because the electron pairs encounter no opposition. When Cooper pairs are warmed, the pairs separate from their correlated motions into individual electrons and the material becomes non-superconducting. The theory supplies experimental means of measuring the energy needed to separate Cooper pairs [http://www.britannica.com/science/BCS-theory].

[[File:Superconductor.gif]]

== See also ==
Liquid Nitrogen Experiments: The Superconductor (Video) https://www.youtube.com/watch?v=o6t2IWHA63o

===References===
http://www.britannica.com/biography/John-Bardeen

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen.jpg

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html

http://www.britannica.com/technology/transistor

http://www.britannica.com/science/BCS-theory

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/imgsol/meis2.gif

John Bardeen

2015-12-03T03:07:38Z

Ajacob30:

Claimed by Alexis Jacob (ajacob30) 12/2/2015

John Bardeen (May 23, 1908-Jan 30, 1991) was an American physicist who was cowinner of the Nobel Prize for physics in 1956 and 1972 [http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html]. The 1956 Nobel Prize was for the joint invention of the transistor with William B. Shockley and Walter H. Brattain. The 1972 Nobel Prize was for developing the theory of superconductivity with Leon N. Cooper and John R. Schrieffer [http://www.britannica.com/biography/John-Bardeen].

[[File:John_Bardeen.jpg]]

===University Education and Career===
Bardeen earned his bachelor's and master's in electrical engineering at the University of Wisconsin, Madison. He received his doctorate in mathermatical physics from Princeton University in 1936. He later became a staff member at eh University of Minnesota, Minneapolis from 1938 to 1941. During World War II, he served as principal physicist at the U.S. Naval Ordinance Laboratory in Washington, D.C. From 1951 to 1975, Bardeen served as a professor of electrical engineering and physics at the University of Illinois, Urbana-Champaign [http://www.britannica.com/biography/John-Bardeen].

==Scientific Contribution==
In 1945, Bardeen joined Bell Laboratories where he researched the electron-conducting properties of semiconductors with his colleagues, Brattain and Shockley. Together on Dec. 23, 1947, they began the electronic revolution with the creation of the transistor. This device allowed computers to be manufactured with smaller and more accessible parts [http://www.britannica.com/biography/John-Bardeen].
In the early 1950s, Bardeen continued research on superconductivity at near absolute temperatures. He created the BCS theory, with Cooper and Schrieffer, to explain the disappearance of electrical resistance in materials near such extreme temperatures [http://www.britannica.com/biography/John-Bardeen].

===Transistor===
A transistor is a semiconductor that amplifies, controls, and generates electrical signals. It is made up of integrated circuits called microchips. Its small size, low heat generation, and power efficiency made it the foundation of the Information Age. The three leads in a transistor are the emitter, collector, and the base which in modern appliances are known as the source, drain, and gate. The electrical signal applied at the base influences the semiconductor's ability to conduct current. The current then flows between the emitter and collector. The rate of flow of current is determined by the input signal at the gate [http://www.britannica.com/technology/transistor].

[[File:Transistor.jpg]]

===Bardeen-Cooper-Schrieffer Theory (BCS Theory)===
BCS theory is a comprehensive theory that explains the behavior of superconducting materials; they lost resistance to the flow of electric current when cooled to temperatures near zero. Superconductors form when electrons in pairs, called Cooper pairs, in a material all have correlated motion. After applying voltage and removing the voltage, the current continues flowing because the electron pairs encounter no opposition. When Cooper pairs are warmed, the pairs separate from their correlated motions into individual electrons and the material becomes non-superconducting. The theory supplies experimental means of measuring the energy needed to separate Cooper pairs [http://www.britannica.com/science/BCS-theory].

[[File:Superconductor.jpg]]

== See also ==
Liquid Nitrogen Experiments: The Superconductor (Video) https://www.youtube.com/watch?v=o6t2IWHA63o

===References===
http://www.britannica.com/biography/John-Bardeen

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen.jpg

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html

http://www.britannica.com/technology/transistor

http://www.britannica.com/science/BCS-theory

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/imgsol/meis2.gif

File:Superconductor.gif

2015-12-03T03:07:22Z

Ajacob30:

John Bardeen

2015-12-03T02:22:11Z

Ajacob30: /* BCS Theory */

Claimed by Alexis Jacob (ajacob30) 12/2/2015

John Bardeen (May 23, 1908-Jan 30, 1991) was an American physicist who was cowinner of the Nobel Prize for physics in 1956 and 1972 [http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html]. The 1956 Nobel Prize was for the joint invention of the transistor with William B. Shockley and Walter H. Brattain. The 1972 Nobel Prize was for developing the theory of superconductivity with Leon N. Cooper and John R. Schrieffer [http://www.britannica.com/biography/John-Bardeen].

[[File:John_Bardeen.jpg]]

===University Education and Career===
Bardeen earned his bachelor's and master's in electrical engineering at the University of Wisconsin, Madison. He received his doctorate in mathermatical physics from Princeton University in 1936. He later became a staff member at eh University of Minnesota, Minneapolis from 1938 to 1941. During World War II, he served as principal physicist at the U.S. Naval Ordinance Laboratory in Washington, D.C. From 1951 to 1975, Bardeen served as a professor of electrical engineering and physics at the University of Illinois, Urbana-Champaign [http://www.britannica.com/biography/John-Bardeen].

==Scientific Contribution==
In 1945, Bardeen joined Bell Laboratories where he researched the electron-conducting properties of semiconductors with his colleagues, Brattain and Shockley. Together on Dec. 23, 1947, they began the electronic revolution with the creation of the transistor. This device allowed computers to be manufactured with smaller and more accessible parts [http://www.britannica.com/biography/John-Bardeen].
In the early 1950s, Bardeen continued research on superconductivity at near absolute temperatures. He created the BCS theory, with Cooper and Schrieffer, to explain the disappearance of electrical resistance in materials near such extreme temperatures [http://www.britannica.com/biography/John-Bardeen].

===Transistor===
A transistor is a semiconductor that amplifies, controls, and generates electrical signals. It is made up of integrated circuits called microchips. Its small size, low heat generation, and power efficiency made it the foundation of the Information Age. The three leads in a transistor are the emitter, collector, and the base which in modern appliances are known as the source, drain, and gate. The electrical signal applied at the base influences the semiconductor's ability to conduct current. The current then flows between the emitter and collector. The rate of flow of current is determined by the input signal at the gate [http://www.britannica.com/technology/transistor].

[[File:Transistor.jpg]]

===Bardeen-Cooper-Schrieffer Theory (BCS Theory)===

== See also ==
Liquid Nitrogen Experiments: The Superconductor (Video) https://www.youtube.com/watch?v=o6t2IWHA63o

===References===
http://www.britannica.com/biography/John-Bardeen

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen.jpg

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html

http://www.britannica.com/technology/transistor

John Bardeen

2015-12-03T02:20:02Z

Ajacob30: /* Transistor */

Claimed by Alexis Jacob (ajacob30) 12/2/2015

John Bardeen (May 23, 1908-Jan 30, 1991) was an American physicist who was cowinner of the Nobel Prize for physics in 1956 and 1972 [http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html]. The 1956 Nobel Prize was for the joint invention of the transistor with William B. Shockley and Walter H. Brattain. The 1972 Nobel Prize was for developing the theory of superconductivity with Leon N. Cooper and John R. Schrieffer [http://www.britannica.com/biography/John-Bardeen].

[[File:John_Bardeen.jpg]]

===University Education and Career===
Bardeen earned his bachelor's and master's in electrical engineering at the University of Wisconsin, Madison. He received his doctorate in mathermatical physics from Princeton University in 1936. He later became a staff member at eh University of Minnesota, Minneapolis from 1938 to 1941. During World War II, he served as principal physicist at the U.S. Naval Ordinance Laboratory in Washington, D.C. From 1951 to 1975, Bardeen served as a professor of electrical engineering and physics at the University of Illinois, Urbana-Champaign [http://www.britannica.com/biography/John-Bardeen].

==Scientific Contribution==
In 1945, Bardeen joined Bell Laboratories where he researched the electron-conducting properties of semiconductors with his colleagues, Brattain and Shockley. Together on Dec. 23, 1947, they began the electronic revolution with the creation of the transistor. This device allowed computers to be manufactured with smaller and more accessible parts [http://www.britannica.com/biography/John-Bardeen].
In the early 1950s, Bardeen continued research on superconductivity at near absolute temperatures. He created the BCS theory, with Cooper and Schrieffer, to explain the disappearance of electrical resistance in materials near such extreme temperatures [http://www.britannica.com/biography/John-Bardeen].

===Transistor===
A transistor is a semiconductor that amplifies, controls, and generates electrical signals. It is made up of integrated circuits called microchips. Its small size, low heat generation, and power efficiency made it the foundation of the Information Age. The three leads in a transistor are the emitter, collector, and the base which in modern appliances are known as the source, drain, and gate. The electrical signal applied at the base influences the semiconductor's ability to conduct current. The current then flows between the emitter and collector. The rate of flow of current is determined by the input signal at the gate [http://www.britannica.com/technology/transistor].

[[File:Transistor.jpg]]

===BCS Theory===

== See also ==
Liquid Nitrogen Experiments: The Superconductor (Video) https://www.youtube.com/watch?v=o6t2IWHA63o

===References===
http://www.britannica.com/biography/John-Bardeen

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen.jpg

http://www.nobelprize.org/nobel_prizes/physics/laureates/1972/bardeen-bio.html

http://www.britannica.com/technology/transistor

John Bardeen

2015-12-03T02:16:54Z

Ajacob30:

John Bardeen

2015-12-03T02:16:02Z

Ajacob30: