Physics Book - User contributions [en]

Moving Point Charge

2015-12-05T02:06:50Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived this relationship from Maxwell's Equations in 1888. The [[Biot-Savart Law]] was named after [[Jean-Baptiste Biot]] and [[Felix Savart]] who, in 1820, showed a needle deflection from a current carrying wire, thus relating electricity and magnetism.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T02:06:11Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived this relationship from Maxwell's Equations in 1888. Separately, the [[Biot-Savart Law]] was named after [[Jean-Baptiste Biot]] and [[Felix Savart]] who, in 1820, showed a needle deflection from a current carrying wire, thus relating electricity and magnetism.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T02:05:29Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived this relationship from Maxwell's Equations in 1888. Separately, the [[Biot-Savart Law]] was named after [[Jean-Baptiste Biot]] and [[Félix Savart]] who, in 1820, showed a needle deflection from a current carrying wire, thus relating electricity and magnetism.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T02:05:16Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived this relationship from Maxwell's Equations in 1888. Separately, the [[Biot-Savart Law]] was named after [[Jean-Baptiste Biot] and [[Félix Savart]] who, in 1820, showed a needle deflection from a current carrying wire, thus relating electricity and magnetism.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T01:17:58Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these relationships from Maxwell's Equations in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T01:16:51Z

Jmoroz3: /* Difficult */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math> T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these equations from Maxwell's Equations in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T01:16:37Z

Jmoroz3: /* Difficult */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 8 cm from the electron, and the angle θ = 33°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page, all with a magnitude of <math> 8.17*10^{-18}</math>T.

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these equations from Maxwell's Equations in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-05T01:11:46Z

Jmoroz3: /* A Mathematical Model */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite <math>Idl</math> in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these equations from Maxwell's Equations in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:13:27Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these equations from Maxwell's Equations in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:12:21Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

[[Oliver Heaviside]] first derived these equations from [[Maxwell's Equations]] in 1888. See the history of the [[Biot-Savart Law]] for information about this derivation.

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:08:08Z

Jmoroz3: /* History */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart Law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:07:48Z

Jmoroz3: /* See also */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]

[[Magnetic Force]]

[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:07:32Z

Jmoroz3: /* See also */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]
[[Magnetic Force]]
[[Right-Hand Rule]]

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:05:14Z

Jmoroz3:

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-04T03:04:27Z

Jmoroz3:

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-03T22:50:55Z

Jmoroz3:

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

[[Biot-Savart Law for Currents]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-03T22:46:09Z

Jmoroz3:

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-02T00:20:30Z

Jmoroz3: /* The Main Idea */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrite Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-02T00:19:41Z

Jmoroz3: /* Difficult */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

[[File:ExampleMCharge.png]]

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-02T00:19:07Z

Jmoroz3: /* Difficult */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product v X r where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-02T00:18:35Z

Jmoroz3: /* Difficult */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product <math> vXr </math> where the v is given.

3. Multiply each respective cross product by the magnitude of charge and <math> mu_0 </math>.

4. In order to find the direction of the magnetic fields, use the [[Right Hand Rule]]. One way to do this is to point your thumb in the direction of the velocity, your pointer finger in the direction of r hat, and look which way your palm is facing in order to find the direction of the magnetic field.

At location P2 and P5 the magnetic field will be zero. P1 will be into the page, P3 will be out of the page, P4 will be out of the page, and P6 will be into the page

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T22:17:08Z

Jmoroz3: /* Difficult */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

'''Solution:'''

1. Find the r vector for each location, using <math> \theta </math> to calculate the x and y components

2. For each r vector, take the cross product <math> vXr </math> where the v is given.

3. Multiply each respective

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:14:24Z

Jmoroz3: /* Examples */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 6*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 34°. Give both magnitude and direction of the magnetic field at locations 1, 2 and 3.

'''Solution:'''

1. Find the r vector for each location, using <math> \theta <math> to calculate the x and y components

2. For each r vector, take the cross product <math> vXr </math> where the v is given.

3. Multiply each respective

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:07:03Z

Jmoroz3: /* Medium */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:06:47Z

Jmoroz3: /* Medium */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 </math> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:06:09Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:05:53Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 </math> or <math>10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:05:16Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 or 10^{-7}</math>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:04:35Z

Jmoroz3: /* Medium */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 or 10^{-7}<math/>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees

[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:04:20Z

Jmoroz3: /* Medium */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 or 10^{-7}<math/>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math> degrees
[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:04:05Z

Jmoroz3: /* Medium */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 or 10^{-7}<math/>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math>degrees
[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T21:03:41Z

Jmoroz3:

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. Don't forget to also multiply this by <math> \mu_0 or 10^{-7}<math/>.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math> T

===Medium===
The electron in the figure below is traveling with a speed of
<math> v = 4*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 7*10^{-10}</math>m and <math>\theta=57 </math>degrees
[[File:Example2vB.png|300x400px]]

'''Solution:'''

1. First split up the velocity in to its x and y components by multiplying the given velocity by cos(57) and sin(57) for x and y respectively.

2. Find r hat and take the cross product of your new velocity vector with r hat.

3. Multiply this by the magnitude of the charge for an electron, as well as by <math> \mu_0 <math/> and then divide this by the <math> r^2 </math>

The final answer will be 0.11 T

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:45:57Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''

1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:45:42Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''
1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.

2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>

3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:45:20Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''
1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:44:38Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''
The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:44:18Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.

'''Solution:'''
The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:43:42Z

Jmoroz3: /* Simple */

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.\

Solution:
The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:43:11Z

Jmoroz3:

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.\

Solution:
The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|300x400px]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:33:44Z

Jmoroz3:

Page claimed by James Moroz
[[User:Jmoroz3|Jmoroz3]] ([[User talk:Jmoroz3|talk]]) 11:47, 20 November 2015 (EST)

This page covers the method of calculating the magnetic field from a moving point charge, derived from the [[Biot-Savart Law]] for magnetic fields.

==The Main Idea==

===A Mathematical Model===

The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:ILxR.png]]

With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.

[[File:Idltoqv.gif]]

With this substitution, the final formula comes out to be:

[[File:BiotSavartv.gif]]

where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.\

Solution:
The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif]] tells us to do.
Crossing these two, we get < 0, 0, 49200>
The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared.

The final answer will be <math> <0, 0, 1.75*10^{-19}> </math>

===Middling===
The electron in the figure below is traveling with a speed of
<math> v = 5*10^6 </math>m/s. What is the magnitude of the magnetic field at location A if r = <math> 8*10^{-10}</math>m and <math>\theta=40 </math>degrees
[[File:Example2vB.png|300x400px]]

===Difficult===
An electron is moving horizontally to the right with speed <math> 5*10^6 </math> m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.

[[File:ExampleMCharge.png]]

==Connectedness==
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.

==History==

The history of the Biot Savart law and its discovery can be found at the [[Biot-Savart Law]].

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Moving Point Charge

2015-12-01T20:12:42Z

Jmoroz3: /* Examples */

Moving Point Charge

2015-12-01T01:14:08Z

Jmoroz3:

Moving Point Charge

2015-12-01T01:13:34Z

Jmoroz3: /* A Mathematical Model */

Moving Point Charge

2015-11-30T22:20:43Z

Jmoroz3: /* Middling */

Moving Point Charge

2015-11-30T22:16:31Z

Jmoroz3: /* Middling */

Moving Point Charge

2015-11-30T22:15:49Z

Jmoroz3: /* Middling */

Moving Point Charge

2015-11-30T22:13:08Z

Jmoroz3: /* Middling */

Moving Point Charge

2015-11-30T22:09:57Z

Jmoroz3:

Moving Point Charge

2015-11-30T22:01:53Z

Jmoroz3: /* Middling */

Moving Point Charge

2015-11-30T22:01:18Z

Jmoroz3: /* Middling */