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2016-04-17T23:24:30Z

Dtran38: /* Moving charges, electron current, and conventional current */

Moving Point Charge

2016-04-17T19:52:29Z

Dtran38:

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
Edited by Diem Tran Spring 2016.
The [[Biot-Savart Law]] for the magnetic field of a moving charge can be quite complex in calculations. The method of calculations can be broken down further into simpler steps.

==The Main Idea==

===A Mathematical Model===

A moving point charge not only has an electric field due to its possession of a charge but also has a magnetic field due to its velocity. The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:BiotSavartv.gif]]

where q is the scalar charge of the particle, v is the vector velocity of the moving particle, and r is the vector distance from the observation location to the position of the moving particle. The magnetic constant in the formula has the value of 1e-7 T(m/A). V × r is a cross product that can be computed by the formula:

[[File:CrossProduct.png]]

A trigonometric equivalence of the above formula is (p)(q)sin(θ)

Which can be written in terms of v and r as: (v)(r)sin(θ)
θ in this formula is the angle between the vectors v and r.

To determine the direction of the resulting vector from a cross product, we use the right hand rule where we align our right-hand fingers so that it can sweep from the vector v to the vector r. Where our thumb points as a result of this alignment is the direction of v × r.
The final direction of the magnetic field will depend on the charge of our particle. If our particle is positively charged, the magnetic field will point in the same direction as v × r. If the particle is negatively charged, the magnetic field will point in the opposite direction as v × r.

The unit of our result will be in Tesla, the unit for a magnetic field.

==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

===Complex===
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.

==Important Applications==
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.

We can use the magnetic field of a single moving charge formula to derive a more practical formula of a short current carrying wire:

[[File:ILxR.png]]

Where dl is a vector pointing in the same direction as the conventional [[current]]
This formula is more applicable to many real life situations where we can have macroscopic objects that can be used to calculate the magnetic field, such as the [[Magnetic Field of a Long Straight Wire]] or a [[Magnetic Field of a Loop]].

We can apply the magnetic field formula to numerous situations by integration.

==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
http://ruh.li/3DMathVectors.html

[[Moving Point Charge]]

Moving Point Charge

2016-04-17T19:51:51Z

Dtran38: /* References */

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
Edited by Diem Tran 2016.
The [[Biot-Savart Law]] for the magnetic field of a moving charge can be quite complex in calculations. The method of calculations can be broken down further into simpler steps.

==The Main Idea==

===A Mathematical Model===

A moving point charge not only has an electric field due to its possession of a charge but also has a magnetic field due to its velocity. The magnetic field of a moving point charge can be found using a derivation of the [[Biot-Savart Law]] for magnetic fields.

[[File:BiotSavartv.gif]]

where q is the scalar charge of the particle, v is the vector velocity of the moving particle, and r is the vector distance from the observation location to the position of the moving particle. The magnetic constant in the formula has the value of 1e-7 T(m/A). V × r is a cross product that can be computed by the formula:

[[File:CrossProduct.png]]

A trigonometric equivalence of the above formula is (p)(q)sin(θ)

Which can be written in terms of v and r as: (v)(r)sin(θ)
θ in this formula is the angle between the vectors v and r.

To determine the direction of the resulting vector from a cross product, we use the right hand rule where we align our right-hand fingers so that it can sweep from the vector v to the vector r. Where our thumb points as a result of this alignment is the direction of v × r.
The final direction of the magnetic field will depend on the charge of our particle. If our particle is positively charged, the magnetic field will point in the same direction as v × r. If the particle is negatively charged, the magnetic field will point in the opposite direction as v × r.

The unit of our result will be in Tesla, the unit for a magnetic field.

==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

===Complex===
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.

==Important Applications==
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.

We can use the magnetic field of a single moving charge formula to derive a more practical formula of a short current carrying wire:

[[File:ILxR.png]]

Where dl is a vector pointing in the same direction as the conventional [[current]]
This formula is more applicable to many real life situations where we can have macroscopic objects that can be used to calculate the magnetic field, such as the [[Magnetic Field of a Long Straight Wire]] or a [[Magnetic Field of a Loop]].

We can apply the magnetic field formula to numerous situations by integration.

==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
http://ruh.li/3DMathVectors.html

[[Moving Point Charge]]

2016-04-17T17:57:54Z

Dtran38:

{{DISPLAYTITLE:Magnetic Field of a Moving Point Charge}}
Claimed by Diem Tran 2016. 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?]]

Main Page

2016-04-17T04:33:52Z

Dtran38: /* Week 7 */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>
*[[Types of Interactions and How to Detect Them]]

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''CLAIMED BY DIPRO CHAKRABORTY'''

'''CLAIMED BY DIPRO CHAKRABORTY'''
'''CLAIMED BY DIPRO CHAKRABORTY'''
'''CLAIMED BY DIPRO CHAKRABORTY'''

'''CLAIMED BY DIPRO CHAKRABORTY'''
====Electric field====
<div class="mw-collapsible-content">

[[Electric field]]

The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

===Simple===
Which way is the electric field going for a negatively charged particle?

[[File:Simple111.png]]

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending
toward the negatively charged particle.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

===Simple===
Which way is the electric field going for a negatively charged particle?

[[File:Simple111.png]]

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending
toward the negatively charged particle.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

===Simple===
Which way is the electric field going for a negatively charged particle?

[[File:Simple111.png]]

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending
toward the negatively charged particle.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} </math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

===Simple===
Which way is the electric field going for a negatively charged particle?

[[File:Simple111.png]]

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending
toward the negatively charged particle.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

===Simple===
Which way is the electric field going for a negatively charged particle?

[[File:Example.jpg]]

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending
toward the negatively charged particle.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the Electric Field is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that
is interacting with the particle. This "virtual force" is in essence the electric field.
===A Mathematical Model===

The electric field can be expressed mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

<math>{\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric
field.

==Examples==

The following examples are to test your basic understanding of Newton's First Law. For more examples that test your knowledge of all three of the laws, click .

===Simple===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

It's easy to see that the only force on the object is acting in the +x direction, with a magnitude of 5 newtons. Therefore, the object does not have a net force of zero or a constant velocity. It will be accelerating in the +x direction.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the First Law of Motion is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
In other (and much simpler) terms, it means that an object at rest stays at rest and an object in in motion stays in motion at a constant velocity unless acted on by an unbalanced net force. It's important to keep in mind that only a difference in affect the velocity of an object. The amount of change in velocity is determined by
===A Mathematical Model===

Newton's first law can be stated mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

Where...

<math>\vec{F_{net}}</math> is the net force from the surroundings.

<math>d\vec{v}</math> is the change in velocity of the system.

<math>dt</math> is the change in time of the system

If we trace this formula from the left to the right, we can see that if the net force on an object is zero, then the change in velocity of an object is also zero. Conversely, if we were given an object and told that its change in momentum is zero, then we can deduce that the net force acting on the object is also zero. Keep in mind, however, that this formula simple deals with the '''change''' in velocity. It does '''not''' mean that the object is at rest, only that its velocity remains constant.

==Examples==

The following examples are to test your basic understanding of Newton's First Law. For more examples that test your knowledge of all three of the laws, click .

===Simple===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

It's easy to see that the only force on the object is acting in the +x direction, with a magnitude of 5 newtons. Therefore, the object does not have a net force of zero or a constant velocity. It will be accelerating in the +x direction.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the First Law of Motion is as follows:
The electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
In other (and much simpler) terms, it means that an object at rest stays at rest and an object in in motion stays in motion at a constant velocity unless acted on by an unbalanced net force. It's important to keep in mind that only a difference in affect the velocity of an object. The amount of change in velocity is determined by
===A Mathematical Model===

Newton's first law can be stated mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

Where...

<math>\vec{F_{net}}</math> is the net force from the surroundings.

<math>d\vec{v}</math> is the change in velocity of the system.

<math>dt</math> is the change in time of the system

If we trace this formula from the left to the right, we can see that if the net force on an object is zero, then the change in velocity of an object is also zero. Conversely, if we were given an object and told that its change in momentum is zero, then we can deduce that the net force acting on the object is also zero. Keep in mind, however, that this formula simple deals with the '''change''' in velocity. It does '''not''' mean that the object is at rest, only that its velocity remains constant.

==Examples==

The following examples are to test your basic understanding of Newton's First Law. For more examples that test your knowledge of all three of the laws, click .

===Simple===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

It's easy to see that the only force on the object is acting in the +x direction, with a magnitude of 5 newtons. Therefore, the object does not have a net force of zero or a constant velocity. It will be accelerating in the +x direction.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

==Connectedness==

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==The Main Idea==
To be exact, the definition of the First Law of Motion is as follows:
Every body persists in its state of rest or of moving with constant speed in a constant direction, except to the extent that it is compelled to change that state by forces acting on it.
In other (and much simpler) terms, it means that an object at rest stays at rest and an object in in motion stays in motion at a constant velocity unless acted on by an unbalanced net force. It's important to keep in mind that only a difference in [http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Determining-the-Net-Force net force] can affect the velocity of an object. The amount of change in velocity is determined by [http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law Newton's Second Law of Motion].

===A Mathematical Model===

Newton's first law can be stated mathematically as follows:

<math>{\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0</math>

Where...

<math>\vec{F_{net}}</math> is the net force from the surroundings.

<math>d\vec{v}</math> is the change in velocity of the system.

<math>dt</math> is the change in time of the system

If we trace this formula from the left to the right, we can see that if the net force on an object is zero, then the change in velocity of an object is also zero. Conversely, if we were given an object and told that its change in momentum is zero, then we can deduce that the net force acting on the object is also zero. Keep in mind, however, that this formula simple deals with the '''change''' in velocity. It does '''not''' mean that the object is at rest, only that its velocity remains constant.

==Examples==

The following examples are to test your basic understanding of Newton's First Law. For more examples that test your knowledge of all three of the laws, click [http://www.physicsclassroom.com/calcpad/newtlaws/problems here].

===Simple===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

[[File:Newtonfirstlawsimple.png|400px]]

It's easy to see that the only force on the object is acting in the +x direction, with a magnitude of 5 newtons. Therefore, the object does not have a net force of zero or a constant velocity. It will be accelerating in the +x direction.

===Middling===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

[[File:Newtonfirstlawmedium.png|400px]]

This example is slightly more difficult, but is still quite trivial. If we sum the forces in the x direction, we see that the net force is 2 newtons in the -x direction. Therefore, the object does not have a constant velocity, and will be accelerating in the -x direction.

===Difficult===
Does the object in the following image have a net force of zero? Does it have a constant velocity?

[[File:Newtonsfirstlawhard.png|400px]]

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are [http://www.physicsclassroom.com/class/vectors/Lesson-1/Independence-of-Perpendicular-Components-of-Motion independent] of each other.

==Connectedness==

[[File:Tablecloth.gif|left|300px|thumb|The "magic trick" of ripping off a table cloth without the plates on top moving is an example of Newton's First Law. The tableware is in a state of rest, and thus want to remain in such a state.]]

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, ''Gravity'', explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.
==History==

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, ''Principles of Philosophy'', the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in ''The Mathematical Principle of Natural Philosophy'', for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.

==Electric Field==
The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction.
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7=== Claimed by Diem Tran
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]] claimed by Hannah Jang
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Resistors*]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

== Part 2: Initial Transient State (Magnetic Field Present) ==

Mobile electrons are subjected to a magnetic field as they flow through the wire. Since electrons are negatively charged, they experience a magnetic force in the downward direction due to the magnetic field. This can be summarized by the equation:

[[File:Mag_force.png]]

See aside for extra help on determining this direction.

==Part 3: Steady State (Magnetic Field Still Present)==

Over time more and more charges are going to build up. As they build up, they will begin to create a charged area on one surface of the conductor. This charged surface will start to oppose the magnetic force that is holding the electrons. Essentially the electrons are being held against the side of the conductor by the magnetic force. As more and more electrons collect together against the surface of the conductor, they start to oppose the magnetic force that’s holding them. This opposing force is called the transverse electric force and is responsible for the existence of the perpendicular electric field. When enough electrons have collected, their combined transverse electric force will be equal in magnitude to the magnetic force that is holding them. At this point, there is no net vertical force pushing more electrons against the surface of the conductor and these electrons will flow normally again. This is called the steady state. As long as the magnetic field remains the same magnitude and in the same direction and the same number of electrons remain pushed against the conductor’s surface, the steady state will be maintained.

[[File:F_perp.png]]

== 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?

===External links===

Internet resources on this topic

<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
[[File:Example.jpg]]

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>