Physics Book - User contributions [en]

Superposition principle

2025-12-01T04:26:39Z

Rsharma443: /* The Main Idea */

'''Claimed by Rithwik Sharma Fall 2025'''

This page explains the superposition principle and brings together examples, models, and applications to make the idea easier to learn.

==The Main Idea==

The superposition principle says that when several influences act on a system, the total response is the sum of the individual responses. For electric fields, this means each charge creates its own field independently, and the net field is found by adding all of them as vectors.

It shows up in many areas of physics and engineering. In circuits, the total voltage at a node can be found by adding contributions from multiple sources. In mechanics, forces from different components of a structure add to give a net reaction. In fields, superposition makes it possible to calculate complex electric and magnetic environments by breaking the problem into simpler pieces.

All in all, the key idea is that each contribution acts independently. Nothing “distorts” another field, so the total is just the vector addition of all of them.

===A Mathematical Model===

The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges. It is important to note that this principle applies to all linear systems, note just those of fields. It has the same net result for mechanics as well. Below are the 2 predominate mathematical models for the principle.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===

Here is a python program that calculates and displays the electric as well as magnetic field at a specific observation location for a '''moving dipole'''. The dipole is a negative and positive charge ''q'' and distance ''s''. Write a porgram that will use the given constants to do this.

# GlowScript 2.0 VPython

magconstant = 1e-7
oofpez = 9e9
q=1.6e-19
s = 1e-9
pluscharge = sphere(pos=vector(-5*s, 0,-s/2), radius=1e-10, color=color.red)
minuscharge = sphere(pos=vector(-5*s, 0, s/2), radius=1e-10, color=color.blue)
velocity = vector(4e4,0,0) # The dipoles cm velocity
robs = vector(0,s,0)

# Initializes two arrows (E and B) at the observation location
E = arrow(pos = robs, axis=vector(0,0,0), color = color.cyan)
B = arrow(pos = robs, axis=vector(0,0,0), color = color.magenta)

# Loop that updates dipole position as well as electric and magnetic field
dt = 1e-18

while pluscharge.pos.x < 10*s:

rate(100)

rplus = robs - pluscharge.pos
rplusmag = mag(rplus)
rplushat = norm(rplus)

Eplus = ((oofpez * q) / (rplusmag ** 2))
Bplus = magconstant * q * cross(velocity, rplushat) / rplusmag ** 2

rminus = robs - minuscharge.pos
rminusmag = mag(rminus)
rminushat = norm(rminus)

Eminus = (oofpez * (-q) / (rminus ** 2)) * rminus
Bminus = (magconstant * (-q) * cross(velocity, rminushat)) / (rminushat ** 2)

#Calculates the new E and B net fields
Enet = Eplus + Eminus
Bnet = Bplus + Bminus

# Updates the E and B fields arrows
E.axis = Enet
B.axis = Bnet
from visual import * #import the visual module

rod = cylinder(pos=(0,2,1), axis=(5,0,0), radius=1)

Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field. Notice the importance of the signs.
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

===Simple===

[[File:Electric_Forces_Fields_P1.JPG]]

Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.

''Answer:''

Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:
<math>\vec{E_1} + \vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C + <math><0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C
<math> = <2\hat{i}+2\hat{j}+0\hat{k}> </math>

Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. Again it is important to note the effect of the signs. Since both components have positive notation, the net result is positive. However if any of the components had a negative direction, it would have been important to note this throughout the answer.

=== Difficult ===

[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Again, sign notation is very important. Note how the unit vector defines the direction of the fields in this equation and example. It is easiest to define the unit vector first. Then proceed to multiply this my the magnitude of the field, as this allows you to account for direction before the calculation of field.

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.

[[File:determinate-structures-18-638.jpeg]]

In a system such as this, the superposition principle is especially useful for finding the individual reactions at each point on the beam as it is known that the net reaction for the entire system is 0.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However they were eventually proved wrong by Joseph Fourier and it is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
*[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

*[http://www.physicsbook.gatech.edu/Superposition_Principle]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

[https://www.youtube.com/watch?v=_8fcT95JV34 Video detailing the general use of the principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

https://www.slideshare.net/tarungehlot1/determinate-structures

[[Fields]]

Superposition principle

2025-12-01T04:25:33Z

Rsharma443: improved main idea, made changes to glowscript and equations, removed redundancy and irrelevant information like "better major like me" jokes

'''Claimed by Rithwik Sharma Fall 2025'''

This page explains the superposition principle and brings together examples, models, and applications to make the idea easier to learn.

==The Main Idea==

The superposition principle says that when several influences act on a system, the total response is the sum of the individual responses. For electric fields, this means each charge creates its own field independently, and the net field is found by adding all of them as vectors.

The superposition principle shows up in many areas of physics and engineering. In circuits, the total voltage at a node can be found by adding contributions from multiple sources. In mechanics, forces from different components of a structure add to give a net reaction. In fields, superposition makes it possible to calculate complex electric and magnetic environments by breaking the problem into simpler pieces.

The key idea is that each contribution acts independently. Nothing “distorts” another field, so the total is just the vector addition of all of them.

===A Mathematical Model===

The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges. It is important to note that this principle applies to all linear systems, note just those of fields. It has the same net result for mechanics as well. Below are the 2 predominate mathematical models for the principle.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===

Here is a python program that calculates and displays the electric as well as magnetic field at a specific observation location for a '''moving dipole'''. The dipole is a negative and positive charge ''q'' and distance ''s''. Write a porgram that will use the given constants to do this.

# GlowScript 2.0 VPython

magconstant = 1e-7
oofpez = 9e9
q=1.6e-19
s = 1e-9
pluscharge = sphere(pos=vector(-5*s, 0,-s/2), radius=1e-10, color=color.red)
minuscharge = sphere(pos=vector(-5*s, 0, s/2), radius=1e-10, color=color.blue)
velocity = vector(4e4,0,0) # The dipoles cm velocity
robs = vector(0,s,0)

# Initializes two arrows (E and B) at the observation location
E = arrow(pos = robs, axis=vector(0,0,0), color = color.cyan)
B = arrow(pos = robs, axis=vector(0,0,0), color = color.magenta)

# Loop that updates dipole position as well as electric and magnetic field
dt = 1e-18

while pluscharge.pos.x < 10*s:

rate(100)

rplus = robs - pluscharge.pos
rplusmag = mag(rplus)
rplushat = norm(rplus)

Eplus = ((oofpez * q) / (rplusmag ** 2))
Bplus = magconstant * q * cross(velocity, rplushat) / rplusmag ** 2

rminus = robs - minuscharge.pos
rminusmag = mag(rminus)
rminushat = norm(rminus)

Eminus = (oofpez * (-q) / (rminus ** 2)) * rminus
Bminus = (magconstant * (-q) * cross(velocity, rminushat)) / (rminushat ** 2)

#Calculates the new E and B net fields
Enet = Eplus + Eminus
Bnet = Bplus + Bminus

# Updates the E and B fields arrows
E.axis = Enet
B.axis = Bnet
from visual import * #import the visual module

rod = cylinder(pos=(0,2,1), axis=(5,0,0), radius=1)

Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field. Notice the importance of the signs.
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

===Simple===

[[File:Electric_Forces_Fields_P1.JPG]]

Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.

''Answer:''

Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:
<math>\vec{E_1} + \vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C + <math><0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C
<math> = <2\hat{i}+2\hat{j}+0\hat{k}> </math>

Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. Again it is important to note the effect of the signs. Since both components have positive notation, the net result is positive. However if any of the components had a negative direction, it would have been important to note this throughout the answer.

=== Difficult ===

[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Again, sign notation is very important. Note how the unit vector defines the direction of the fields in this equation and example. It is easiest to define the unit vector first. Then proceed to multiply this my the magnitude of the field, as this allows you to account for direction before the calculation of field.

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.

[[File:determinate-structures-18-638.jpeg]]

In a system such as this, the superposition principle is especially useful for finding the individual reactions at each point on the beam as it is known that the net reaction for the entire system is 0.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However they were eventually proved wrong by Joseph Fourier and it is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
*[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

*[http://www.physicsbook.gatech.edu/Superposition_Principle]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

[https://www.youtube.com/watch?v=_8fcT95JV34 Video detailing the general use of the principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

https://www.slideshare.net/tarungehlot1/determinate-structures

[[Fields]]

Main Page

2025-12-01T04:21:53Z

Rsharma443: /* Electric field */

__NOTOC__
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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?
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#Add content to that topic or improve the quality of what is already there.
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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]
* A collection of 26 volumes of lecture notes by Prof. Wheeler of Reed College [https://rdc.reed.edu/c/wheeler/home/]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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 listing of [[Notable Scientist]] with links to their individual pages

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

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====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">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<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]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[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>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Jeet Bhatkar====

====Energy Principle====
The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.
<div class="mw-collapsible-content">

*[[Kinetic Energy]]
Kinetic energy is the energy an object possesses due to its motion.
*[[Work/Energy]]
Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.
*[[The Energy Principle]]
Work and energy are closely related concepts. Work (
𝑊) done on an object is defined as the force (
𝐹) applied to the object multiplied by the displacement (
𝑑) of the object in the direction of the force:
The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.
*[[Conservation of Energy]]
The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.
</div>
</div>

===Week 8===
<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>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[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>

===Week 10===
<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]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<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">
====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>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[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 Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<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>

===Week 15===
<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]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</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">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

== Electric force ==
'''Jeet Bhatkar – Fall 2025'''

== Big Idea ==
Electric force is the interaction between objects that have electric charge. It is:

* '''Long-range''': acts even when charges do not touch
* '''Vector-valued''': has magnitude and direction
* '''Superposable''': forces from many charges add as vectors

At the intro level, the electric force between two point charges is described by Coulomb’s law, the electrostatic analog of the gravitational force between masses.

== Key Equations ==

'''Coulomb’s Law (magnitude)'''
:[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]

* [math]\displaystyle{F}[/math] = magnitude of the electric force
* [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
* [math]\displaystyle{q_1, q_2}[/math] = charges (C)
* [math]\displaystyle{r}[/math] = separation between the charges (m)

'''Coulomb’s Law (vector form)'''
:[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]

* [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
* [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2

'''Relation to Electric Field'''
:[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]

Once you know [math]\displaystyle{\vec{E}}[/math] at a point, you can find the force on any charge [math]\displaystyle{q}[/math] placed there.

== Conceptual Picture ==

'''Sign of charges'''
* Like charges (both positive or both negative) → '''repel'''
* Unlike charges (one positive, one negative) → '''attract'''

'''Distance dependence'''
* Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.

'''Superposition principle'''
If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge:
[math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].

'''Electric vs. gravitational force'''
* Both follow inverse-square laws
* Gravity is always attractive; electric force can be attractive or repulsive
* Electric forces are usually much stronger at the particle scale

== Worked Example 1: Two Point Charges on a Line ==

'''Problem.'''
Two charges are placed on the x-axis:

* [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
* [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]

What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?

'''Solution (outline).'''

# Distance between charges:
[math]\displaystyle{ r = 0.40\ \text{m} }[/math].

# Magnitude using Coulomb’s law:
[math]\displaystyle{
F = k \dfrac{|q_1 q_2|}{r^2}
= (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2}
}[/math]

# Sign and direction:
* [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is '''attractive'''
* On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
* Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the '''−x''' direction

You can finish by computing the numerical value and writing it as a vector, e.g. [math]\displaystyle{\vec{F}_{2 \leftarrow 1} = -F\,\hat{x}}[/math].

== Worked Example 2: Superposition with Three Charges ==

'''Problem.'''
Three equal charges [math]\displaystyle{q}[/math] are at the corners of an equilateral triangle of side [math]\displaystyle{a}[/math]. What is the net force on one of the charges?

'''Idea (no full algebra).'''

* Each of the other two charges exerts a force of magnitude
[math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]
* The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
* Use vector addition:
* Add components along the symmetry axis
* Perpendicular components cancel by symmetry

This shows how symmetry plus superposition simplify the vector addition.

== Computational Model (GlowScript) ==

Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.

You can:
* Paste this into a new GlowScript Trinket (Python / VPython),
* Get the embed code from Trinket,
* Embed that code into this page so it runs directly here.

<syntaxhighlight lang="python">
from vpython import *

# constant
k = 8.99e9 # N·m^2/C^2

# scene setup
scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"

# charges (positions in meters, charges in coulombs)
q1 = 2e-6 # C (blue, fixed)
q2 = -3e-6 # C (red, movable)

charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue)
charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)

# arrow to show force on q2 due to q1
F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))

def electric_force(q1, q2, r1, r2):
r_vec = r2 - r1
r = mag(r_vec)
if r == 0:
return vector(0, 0, 0)
F_mag = k * q1 * q2 / r**2
return F_mag * norm(r_vec)

dragging = False

def down():
global dragging
if scene.mouse.pick is charge2:
dragging = True

def up():
global dragging
dragging = False

scene.bind("mousedown", lambda evt: down())
scene.bind("mouseup", lambda evt: up())

while True:
rate(60)

if dragging:
# move the red charge with the mouse in the x-y plane
m = scene.mouse.pos
charge2.pos = vector(m.x, m.y, 0)

F = electric_force(q1, q2, charge1.pos, charge2.pos)

# update arrow to show force on q2
F_arrow.pos = charge2.pos
# scale arrow length for visibility (purely visual)
F_arrow.axis = F * 1e7
</syntaxhighlight>

You can extend this model to include more charges or show the net force on a test charge at different locations.

== Common Mistakes and How to Avoid Them ==

* '''Forgetting that force is a vector.'''
Always draw a diagram and keep track of directions. Use components in 2D/3D.
* '''Dropping the absolute value in the magnitude formula.'''
[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.
* '''Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].'''
The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].
* '''Using wrong units.'''
Convert microcoulombs to coulombs, centimeters to meters, etc.
[math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].
* '''Trying to memorize instead of understand.'''
Focus on inverse-square behavior, sign of charges, and superposition.

== Connections to Other Topics ==

* '''Electric Field''' – Electric force per unit charge is the electric field:
[math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].
* '''Potential Energy and Electric Potential''' – Work done by electric forces leads to electric potential energy and voltage.
* '''Lorentz Force''' – The full force on a moving charge also includes magnetic fields:
[math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].
This page focuses on the electric part.

== Practice Problems ==

You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.

# Two charges of [math]\displaystyle{+2.0\ \mu\text{C}}[/math] and [math]\displaystyle{+5.0\ \mu\text{C}}[/math] are 0.30 m apart.
* (a) Find the magnitude of the force on each charge.
* (b) Is the force attractive or repulsive? Explain.

# A charge [math]\displaystyle{q_1 = +4.0\ \mu\text{C}}[/math] is at the origin and [math]\displaystyle{q_2 = -1.0\ \mu\text{C}}[/math] is at [math]\displaystyle{x = 0.20\ \text{m}}[/math].
* Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).
* Verify that Newton’s third law holds (forces are equal and opposite).

# Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].
* Find the net force on one of the corner charges.
* Use symmetry to simplify the vector addition.

# A particle with charge [math]\displaystyle{q = -1.6 \times 10^{-19}\ \text{C}}[/math] experiences an electric force of [math]\displaystyle{3.2 \times 10^{-14}\ \text{N}}[/math] in the +y direction.
* (a) What is the electric field at that point (magnitude and direction)?
* (b) If the charge were positive instead, what would the force direction be?

== What to Review Before an Exam ==

* Determine force direction from a diagram, not just from algebra
* Practice vector addition of multiple forces
* Do quick estimates: “If I double the distance, what happens to the force?”
* Know the difference between:
* Force between charges (Coulomb’s law)
* Electric field
* Electric potential energy

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====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">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</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]]
</div>
</div>

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

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

*[[Current]]

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Curved 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 field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</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">

====Circuitry Basics====
<div class="mw-collapsible-content">
*[[Understanding Fundamentals of Current, Voltage, and Resistance]]
</div>
</div>

<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">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

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

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[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]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</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]]
*[[Motors and Generators]]
*[[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">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====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]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<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">
*[[Classical Physics]]
</div>
</div>

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

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Twin Paradox]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<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]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

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

===Week 10===
<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 11===
<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 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Thermodynamics====
<div class="mw-collapsible-content">
*[[Maxwell Relations]]
*[[Brownian Motion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
*[[Radioactive Decay Processes]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Solid-State/Condensed Matter Physics====
<div class="mw-collapsible-content">
*[[What is Condensed Matter]]
*[[Crystalline Structures]]
*[[Electric-Band Structure]]
</div>
</div>

Main Page

2025-12-01T04:21:22Z

Rsharma443: /* Electric field */

__NOTOC__
= '''Georgia Tech Student 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]
* A collection of 26 volumes of lecture notes by Prof. Wheeler of Reed College [https://rdc.reed.edu/c/wheeler/home/]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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 listing of [[Notable Scientist]] with links to their individual pages

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

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====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">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<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]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[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>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Jeet Bhatkar====

====Energy Principle====
The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.
<div class="mw-collapsible-content">

*[[Kinetic Energy]]
Kinetic energy is the energy an object possesses due to its motion.
*[[Work/Energy]]
Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.
*[[The Energy Principle]]
Work and energy are closely related concepts. Work (
𝑊) done on an object is defined as the force (
𝐹) applied to the object multiplied by the displacement (
𝑑) of the object in the direction of the force:
The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.
*[[Conservation of Energy]]
The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.
</div>
</div>

===Week 8===
<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>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[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>

===Week 10===
<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]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<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">
====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>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[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 Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<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>

===Week 15===
<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]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</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">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
RITHWIK SHARMA FALL 2025
*[[Electric Field]]
An electric field shows how a charged object pushes or pulls on other charges around it. The field points in the direction a positive charge would move, and its strength depends on how much charge is creating it and how far away you are.
*[[Electric Field and Electric Potential]]
Electric potential describes how much energy per charge is stored at a point in space. The electric field tells you how that potential changes from one point to another. Steeper changes in potential create stronger electric fields.
</div>
</div>

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

== Electric force ==
'''Jeet Bhatkar – Fall 2025'''

== Big Idea ==
Electric force is the interaction between objects that have electric charge. It is:

* '''Long-range''': acts even when charges do not touch
* '''Vector-valued''': has magnitude and direction
* '''Superposable''': forces from many charges add as vectors

At the intro level, the electric force between two point charges is described by Coulomb’s law, the electrostatic analog of the gravitational force between masses.

== Key Equations ==

'''Coulomb’s Law (magnitude)'''
:[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]

* [math]\displaystyle{F}[/math] = magnitude of the electric force
* [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
* [math]\displaystyle{q_1, q_2}[/math] = charges (C)
* [math]\displaystyle{r}[/math] = separation between the charges (m)

'''Coulomb’s Law (vector form)'''
:[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]

* [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
* [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2

'''Relation to Electric Field'''
:[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]

Once you know [math]\displaystyle{\vec{E}}[/math] at a point, you can find the force on any charge [math]\displaystyle{q}[/math] placed there.

== Conceptual Picture ==

'''Sign of charges'''
* Like charges (both positive or both negative) → '''repel'''
* Unlike charges (one positive, one negative) → '''attract'''

'''Distance dependence'''
* Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.

'''Superposition principle'''
If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge:
[math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].

'''Electric vs. gravitational force'''
* Both follow inverse-square laws
* Gravity is always attractive; electric force can be attractive or repulsive
* Electric forces are usually much stronger at the particle scale

== Worked Example 1: Two Point Charges on a Line ==

'''Problem.'''
Two charges are placed on the x-axis:

* [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
* [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]

What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?

'''Solution (outline).'''

# Distance between charges:
[math]\displaystyle{ r = 0.40\ \text{m} }[/math].

# Magnitude using Coulomb’s law:
[math]\displaystyle{
F = k \dfrac{|q_1 q_2|}{r^2}
= (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2}
}[/math]

# Sign and direction:
* [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is '''attractive'''
* On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
* Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the '''−x''' direction

You can finish by computing the numerical value and writing it as a vector, e.g. [math]\displaystyle{\vec{F}_{2 \leftarrow 1} = -F\,\hat{x}}[/math].

== Worked Example 2: Superposition with Three Charges ==

'''Problem.'''
Three equal charges [math]\displaystyle{q}[/math] are at the corners of an equilateral triangle of side [math]\displaystyle{a}[/math]. What is the net force on one of the charges?

'''Idea (no full algebra).'''

* Each of the other two charges exerts a force of magnitude
[math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]
* The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
* Use vector addition:
* Add components along the symmetry axis
* Perpendicular components cancel by symmetry

This shows how symmetry plus superposition simplify the vector addition.

== Computational Model (GlowScript) ==

Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.

You can:
* Paste this into a new GlowScript Trinket (Python / VPython),
* Get the embed code from Trinket,
* Embed that code into this page so it runs directly here.

<syntaxhighlight lang="python">
from vpython import *

# constant
k = 8.99e9 # N·m^2/C^2

# scene setup
scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"

# charges (positions in meters, charges in coulombs)
q1 = 2e-6 # C (blue, fixed)
q2 = -3e-6 # C (red, movable)

charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue)
charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)

# arrow to show force on q2 due to q1
F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))

def electric_force(q1, q2, r1, r2):
r_vec = r2 - r1
r = mag(r_vec)
if r == 0:
return vector(0, 0, 0)
F_mag = k * q1 * q2 / r**2
return F_mag * norm(r_vec)

dragging = False

def down():
global dragging
if scene.mouse.pick is charge2:
dragging = True

def up():
global dragging
dragging = False

scene.bind("mousedown", lambda evt: down())
scene.bind("mouseup", lambda evt: up())

while True:
rate(60)

if dragging:
# move the red charge with the mouse in the x-y plane
m = scene.mouse.pos
charge2.pos = vector(m.x, m.y, 0)

F = electric_force(q1, q2, charge1.pos, charge2.pos)

# update arrow to show force on q2
F_arrow.pos = charge2.pos
# scale arrow length for visibility (purely visual)
F_arrow.axis = F * 1e7
</syntaxhighlight>

You can extend this model to include more charges or show the net force on a test charge at different locations.

== Common Mistakes and How to Avoid Them ==

* '''Forgetting that force is a vector.'''
Always draw a diagram and keep track of directions. Use components in 2D/3D.
* '''Dropping the absolute value in the magnitude formula.'''
[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.
* '''Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].'''
The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].
* '''Using wrong units.'''
Convert microcoulombs to coulombs, centimeters to meters, etc.
[math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].
* '''Trying to memorize instead of understand.'''
Focus on inverse-square behavior, sign of charges, and superposition.

== Connections to Other Topics ==

* '''Electric Field''' – Electric force per unit charge is the electric field:
[math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].
* '''Potential Energy and Electric Potential''' – Work done by electric forces leads to electric potential energy and voltage.
* '''Lorentz Force''' – The full force on a moving charge also includes magnetic fields:
[math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].
This page focuses on the electric part.

== Practice Problems ==

You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.

# Two charges of [math]\displaystyle{+2.0\ \mu\text{C}}[/math] and [math]\displaystyle{+5.0\ \mu\text{C}}[/math] are 0.30 m apart.
* (a) Find the magnitude of the force on each charge.
* (b) Is the force attractive or repulsive? Explain.

# A charge [math]\displaystyle{q_1 = +4.0\ \mu\text{C}}[/math] is at the origin and [math]\displaystyle{q_2 = -1.0\ \mu\text{C}}[/math] is at [math]\displaystyle{x = 0.20\ \text{m}}[/math].
* Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).
* Verify that Newton’s third law holds (forces are equal and opposite).

# Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].
* Find the net force on one of the corner charges.
* Use symmetry to simplify the vector addition.

# A particle with charge [math]\displaystyle{q = -1.6 \times 10^{-19}\ \text{C}}[/math] experiences an electric force of [math]\displaystyle{3.2 \times 10^{-14}\ \text{N}}[/math] in the +y direction.
* (a) What is the electric field at that point (magnitude and direction)?
* (b) If the charge were positive instead, what would the force direction be?

== What to Review Before an Exam ==

* Determine force direction from a diagram, not just from algebra
* Practice vector addition of multiple forces
* Do quick estimates: “If I double the distance, what happens to the force?”
* Know the difference between:
* Force between charges (Coulomb’s law)
* Electric field
* Electric potential energy

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====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">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</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]]
</div>
</div>

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

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

*[[Current]]

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Curved 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 field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</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">

====Circuitry Basics====
<div class="mw-collapsible-content">
*[[Understanding Fundamentals of Current, Voltage, and Resistance]]
</div>
</div>

<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">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

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

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[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]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</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]]
*[[Motors and Generators]]
*[[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">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====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]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<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">
*[[Classical Physics]]
</div>
</div>

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

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Twin Paradox]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<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]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

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

===Week 10===
<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 11===
<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 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Thermodynamics====
<div class="mw-collapsible-content">
*[[Maxwell Relations]]
*[[Brownian Motion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
*[[Radioactive Decay Processes]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Solid-State/Condensed Matter Physics====
<div class="mw-collapsible-content">
*[[What is Condensed Matter]]
*[[Crystalline Structures]]
*[[Electric-Band Structure]]
</div>
</div>

Main Page

2025-12-01T04:21:05Z

Rsharma443: /* 3D Vectors */

__NOTOC__
= '''Georgia Tech Student 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]
* A collection of 26 volumes of lecture notes by Prof. Wheeler of Reed College [https://rdc.reed.edu/c/wheeler/home/]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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 listing of [[Notable Scientist]] with links to their individual pages

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

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====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">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<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]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[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>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Jeet Bhatkar====

====Energy Principle====
The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.
<div class="mw-collapsible-content">

*[[Kinetic Energy]]
Kinetic energy is the energy an object possesses due to its motion.
*[[Work/Energy]]
Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.
*[[The Energy Principle]]
Work and energy are closely related concepts. Work (
𝑊) done on an object is defined as the force (
𝐹) applied to the object multiplied by the displacement (
𝑑) of the object in the direction of the force:
The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.
*[[Conservation of Energy]]
The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.
</div>
</div>

===Week 8===
<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>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[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>

===Week 10===
<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]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<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">
====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>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[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 Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<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>

===Week 15===
<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]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</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">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
An electric field shows how a charged object pushes or pulls on other charges around it. The field points in the direction a positive charge would move, and its strength depends on how much charge is creating it and how far away you are.
*[[Electric Field and Electric Potential]]
Electric potential describes how much energy per charge is stored at a point in space. The electric field tells you how that potential changes from one point to another. Steeper changes in potential create stronger electric fields.
</div>
</div>

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

== Electric force ==
'''Jeet Bhatkar – Fall 2025'''

== Big Idea ==
Electric force is the interaction between objects that have electric charge. It is:

* '''Long-range''': acts even when charges do not touch
* '''Vector-valued''': has magnitude and direction
* '''Superposable''': forces from many charges add as vectors

At the intro level, the electric force between two point charges is described by Coulomb’s law, the electrostatic analog of the gravitational force between masses.

== Key Equations ==

'''Coulomb’s Law (magnitude)'''
:[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]

* [math]\displaystyle{F}[/math] = magnitude of the electric force
* [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
* [math]\displaystyle{q_1, q_2}[/math] = charges (C)
* [math]\displaystyle{r}[/math] = separation between the charges (m)

'''Coulomb’s Law (vector form)'''
:[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]

* [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
* [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2

'''Relation to Electric Field'''
:[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]

Once you know [math]\displaystyle{\vec{E}}[/math] at a point, you can find the force on any charge [math]\displaystyle{q}[/math] placed there.

== Conceptual Picture ==

'''Sign of charges'''
* Like charges (both positive or both negative) → '''repel'''
* Unlike charges (one positive, one negative) → '''attract'''

'''Distance dependence'''
* Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.

'''Superposition principle'''
If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge:
[math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].

'''Electric vs. gravitational force'''
* Both follow inverse-square laws
* Gravity is always attractive; electric force can be attractive or repulsive
* Electric forces are usually much stronger at the particle scale

== Worked Example 1: Two Point Charges on a Line ==

'''Problem.'''
Two charges are placed on the x-axis:

* [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
* [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]

What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?

'''Solution (outline).'''

# Distance between charges:
[math]\displaystyle{ r = 0.40\ \text{m} }[/math].

# Magnitude using Coulomb’s law:
[math]\displaystyle{
F = k \dfrac{|q_1 q_2|}{r^2}
= (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2}
}[/math]

# Sign and direction:
* [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is '''attractive'''
* On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
* Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the '''−x''' direction

You can finish by computing the numerical value and writing it as a vector, e.g. [math]\displaystyle{\vec{F}_{2 \leftarrow 1} = -F\,\hat{x}}[/math].

== Worked Example 2: Superposition with Three Charges ==

'''Problem.'''
Three equal charges [math]\displaystyle{q}[/math] are at the corners of an equilateral triangle of side [math]\displaystyle{a}[/math]. What is the net force on one of the charges?

'''Idea (no full algebra).'''

* Each of the other two charges exerts a force of magnitude
[math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]
* The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
* Use vector addition:
* Add components along the symmetry axis
* Perpendicular components cancel by symmetry

This shows how symmetry plus superposition simplify the vector addition.

== Computational Model (GlowScript) ==

Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.

You can:
* Paste this into a new GlowScript Trinket (Python / VPython),
* Get the embed code from Trinket,
* Embed that code into this page so it runs directly here.

<syntaxhighlight lang="python">
from vpython import *

# constant
k = 8.99e9 # N·m^2/C^2

# scene setup
scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"

# charges (positions in meters, charges in coulombs)
q1 = 2e-6 # C (blue, fixed)
q2 = -3e-6 # C (red, movable)

charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue)
charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)

# arrow to show force on q2 due to q1
F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))

def electric_force(q1, q2, r1, r2):
r_vec = r2 - r1
r = mag(r_vec)
if r == 0:
return vector(0, 0, 0)
F_mag = k * q1 * q2 / r**2
return F_mag * norm(r_vec)

dragging = False

def down():
global dragging
if scene.mouse.pick is charge2:
dragging = True

def up():
global dragging
dragging = False

scene.bind("mousedown", lambda evt: down())
scene.bind("mouseup", lambda evt: up())

while True:
rate(60)

if dragging:
# move the red charge with the mouse in the x-y plane
m = scene.mouse.pos
charge2.pos = vector(m.x, m.y, 0)

F = electric_force(q1, q2, charge1.pos, charge2.pos)

# update arrow to show force on q2
F_arrow.pos = charge2.pos
# scale arrow length for visibility (purely visual)
F_arrow.axis = F * 1e7
</syntaxhighlight>

You can extend this model to include more charges or show the net force on a test charge at different locations.

== Common Mistakes and How to Avoid Them ==

* '''Forgetting that force is a vector.'''
Always draw a diagram and keep track of directions. Use components in 2D/3D.
* '''Dropping the absolute value in the magnitude formula.'''
[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.
* '''Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].'''
The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].
* '''Using wrong units.'''
Convert microcoulombs to coulombs, centimeters to meters, etc.
[math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].
* '''Trying to memorize instead of understand.'''
Focus on inverse-square behavior, sign of charges, and superposition.

== Connections to Other Topics ==

* '''Electric Field''' – Electric force per unit charge is the electric field:
[math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].
* '''Potential Energy and Electric Potential''' – Work done by electric forces leads to electric potential energy and voltage.
* '''Lorentz Force''' – The full force on a moving charge also includes magnetic fields:
[math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].
This page focuses on the electric part.

== Practice Problems ==

You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.

# Two charges of [math]\displaystyle{+2.0\ \mu\text{C}}[/math] and [math]\displaystyle{+5.0\ \mu\text{C}}[/math] are 0.30 m apart.
* (a) Find the magnitude of the force on each charge.
* (b) Is the force attractive or repulsive? Explain.

# A charge [math]\displaystyle{q_1 = +4.0\ \mu\text{C}}[/math] is at the origin and [math]\displaystyle{q_2 = -1.0\ \mu\text{C}}[/math] is at [math]\displaystyle{x = 0.20\ \text{m}}[/math].
* Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).
* Verify that Newton’s third law holds (forces are equal and opposite).

# Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].
* Find the net force on one of the corner charges.
* Use symmetry to simplify the vector addition.

# A particle with charge [math]\displaystyle{q = -1.6 \times 10^{-19}\ \text{C}}[/math] experiences an electric force of [math]\displaystyle{3.2 \times 10^{-14}\ \text{N}}[/math] in the +y direction.
* (a) What is the electric field at that point (magnitude and direction)?
* (b) If the charge were positive instead, what would the force direction be?

== What to Review Before an Exam ==

* Determine force direction from a diagram, not just from algebra
* Practice vector addition of multiple forces
* Do quick estimates: “If I double the distance, what happens to the force?”
* Know the difference between:
* Force between charges (Coulomb’s law)
* Electric field
* Electric potential energy

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====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">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</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]]
</div>
</div>

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

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

*[[Current]]

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Curved 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 field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</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">

====Circuitry Basics====
<div class="mw-collapsible-content">
*[[Understanding Fundamentals of Current, Voltage, and Resistance]]
</div>
</div>

<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">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

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

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[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]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</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]]
*[[Motors and Generators]]
*[[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">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====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]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<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">
*[[Classical Physics]]
</div>
</div>

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

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Twin Paradox]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<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]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

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

===Week 10===
<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 11===
<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 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Thermodynamics====
<div class="mw-collapsible-content">
*[[Maxwell Relations]]
*[[Brownian Motion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
*[[Radioactive Decay Processes]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Solid-State/Condensed Matter Physics====
<div class="mw-collapsible-content">
*[[What is Condensed Matter]]
*[[Crystalline Structures]]
*[[Electric-Band Structure]]
</div>
</div>

Main Page

2025-12-01T04:20:41Z

Rsharma443: /* Electric field */

__NOTOC__
= '''Georgia Tech Student 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]
* A collection of 26 volumes of lecture notes by Prof. Wheeler of Reed College [https://rdc.reed.edu/c/wheeler/home/]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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 listing of [[Notable Scientist]] with links to their individual pages

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

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====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">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<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]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[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>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Jeet Bhatkar====

====Energy Principle====
The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.
<div class="mw-collapsible-content">

*[[Kinetic Energy]]
Kinetic energy is the energy an object possesses due to its motion.
*[[Work/Energy]]
Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.
*[[The Energy Principle]]
Work and energy are closely related concepts. Work (
𝑊) done on an object is defined as the force (
𝐹) applied to the object multiplied by the displacement (
𝑑) of the object in the direction of the force:
The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.
*[[Conservation of Energy]]
The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.
</div>
</div>

===Week 8===
<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>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[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>

===Week 10===
<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]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<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">
====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>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[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 Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<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>

===Week 15===
<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]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</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">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

RITHWIK SHARMA FALL 2025

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
An electric field shows how a charged object pushes or pulls on other charges around it. The field points in the direction a positive charge would move, and its strength depends on how much charge is creating it and how far away you are.
*[[Electric Field and Electric Potential]]
Electric potential describes how much energy per charge is stored at a point in space. The electric field tells you how that potential changes from one point to another. Steeper changes in potential create stronger electric fields.
</div>
</div>

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

== Electric force ==
'''Jeet Bhatkar – Fall 2025'''

== Big Idea ==
Electric force is the interaction between objects that have electric charge. It is:

* '''Long-range''': acts even when charges do not touch
* '''Vector-valued''': has magnitude and direction
* '''Superposable''': forces from many charges add as vectors

At the intro level, the electric force between two point charges is described by Coulomb’s law, the electrostatic analog of the gravitational force between masses.

== Key Equations ==

'''Coulomb’s Law (magnitude)'''
:[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]

* [math]\displaystyle{F}[/math] = magnitude of the electric force
* [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
* [math]\displaystyle{q_1, q_2}[/math] = charges (C)
* [math]\displaystyle{r}[/math] = separation between the charges (m)

'''Coulomb’s Law (vector form)'''
:[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]

* [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
* [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2

'''Relation to Electric Field'''
:[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]

Once you know [math]\displaystyle{\vec{E}}[/math] at a point, you can find the force on any charge [math]\displaystyle{q}[/math] placed there.

== Conceptual Picture ==

'''Sign of charges'''
* Like charges (both positive or both negative) → '''repel'''
* Unlike charges (one positive, one negative) → '''attract'''

'''Distance dependence'''
* Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.

'''Superposition principle'''
If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge:
[math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].

'''Electric vs. gravitational force'''
* Both follow inverse-square laws
* Gravity is always attractive; electric force can be attractive or repulsive
* Electric forces are usually much stronger at the particle scale

== Worked Example 1: Two Point Charges on a Line ==

'''Problem.'''
Two charges are placed on the x-axis:

* [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
* [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]

What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?

'''Solution (outline).'''

# Distance between charges:
[math]\displaystyle{ r = 0.40\ \text{m} }[/math].

# Magnitude using Coulomb’s law:
[math]\displaystyle{
F = k \dfrac{|q_1 q_2|}{r^2}
= (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2}
}[/math]

# Sign and direction:
* [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is '''attractive'''
* On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
* Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the '''−x''' direction

You can finish by computing the numerical value and writing it as a vector, e.g. [math]\displaystyle{\vec{F}_{2 \leftarrow 1} = -F\,\hat{x}}[/math].

== Worked Example 2: Superposition with Three Charges ==

'''Problem.'''
Three equal charges [math]\displaystyle{q}[/math] are at the corners of an equilateral triangle of side [math]\displaystyle{a}[/math]. What is the net force on one of the charges?

'''Idea (no full algebra).'''

* Each of the other two charges exerts a force of magnitude
[math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]
* The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
* Use vector addition:
* Add components along the symmetry axis
* Perpendicular components cancel by symmetry

This shows how symmetry plus superposition simplify the vector addition.

== Computational Model (GlowScript) ==

Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.

You can:
* Paste this into a new GlowScript Trinket (Python / VPython),
* Get the embed code from Trinket,
* Embed that code into this page so it runs directly here.

<syntaxhighlight lang="python">
from vpython import *

# constant
k = 8.99e9 # N·m^2/C^2

# scene setup
scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"

# charges (positions in meters, charges in coulombs)
q1 = 2e-6 # C (blue, fixed)
q2 = -3e-6 # C (red, movable)

charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue)
charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)

# arrow to show force on q2 due to q1
F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))

def electric_force(q1, q2, r1, r2):
r_vec = r2 - r1
r = mag(r_vec)
if r == 0:
return vector(0, 0, 0)
F_mag = k * q1 * q2 / r**2
return F_mag * norm(r_vec)

dragging = False

def down():
global dragging
if scene.mouse.pick is charge2:
dragging = True

def up():
global dragging
dragging = False

scene.bind("mousedown", lambda evt: down())
scene.bind("mouseup", lambda evt: up())

while True:
rate(60)

if dragging:
# move the red charge with the mouse in the x-y plane
m = scene.mouse.pos
charge2.pos = vector(m.x, m.y, 0)

F = electric_force(q1, q2, charge1.pos, charge2.pos)

# update arrow to show force on q2
F_arrow.pos = charge2.pos
# scale arrow length for visibility (purely visual)
F_arrow.axis = F * 1e7
</syntaxhighlight>

You can extend this model to include more charges or show the net force on a test charge at different locations.

== Common Mistakes and How to Avoid Them ==

* '''Forgetting that force is a vector.'''
Always draw a diagram and keep track of directions. Use components in 2D/3D.
* '''Dropping the absolute value in the magnitude formula.'''
[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.
* '''Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].'''
The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].
* '''Using wrong units.'''
Convert microcoulombs to coulombs, centimeters to meters, etc.
[math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].
* '''Trying to memorize instead of understand.'''
Focus on inverse-square behavior, sign of charges, and superposition.

== Connections to Other Topics ==

* '''Electric Field''' – Electric force per unit charge is the electric field:
[math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].
* '''Potential Energy and Electric Potential''' – Work done by electric forces leads to electric potential energy and voltage.
* '''Lorentz Force''' – The full force on a moving charge also includes magnetic fields:
[math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].
This page focuses on the electric part.

== Practice Problems ==

You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.

# Two charges of [math]\displaystyle{+2.0\ \mu\text{C}}[/math] and [math]\displaystyle{+5.0\ \mu\text{C}}[/math] are 0.30 m apart.
* (a) Find the magnitude of the force on each charge.
* (b) Is the force attractive or repulsive? Explain.

# A charge [math]\displaystyle{q_1 = +4.0\ \mu\text{C}}[/math] is at the origin and [math]\displaystyle{q_2 = -1.0\ \mu\text{C}}[/math] is at [math]\displaystyle{x = 0.20\ \text{m}}[/math].
* Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).
* Verify that Newton’s third law holds (forces are equal and opposite).

# Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].
* Find the net force on one of the corner charges.
* Use symmetry to simplify the vector addition.

# A particle with charge [math]\displaystyle{q = -1.6 \times 10^{-19}\ \text{C}}[/math] experiences an electric force of [math]\displaystyle{3.2 \times 10^{-14}\ \text{N}}[/math] in the +y direction.
* (a) What is the electric field at that point (magnitude and direction)?
* (b) If the charge were positive instead, what would the force direction be?

== What to Review Before an Exam ==

* Determine force direction from a diagram, not just from algebra
* Practice vector addition of multiple forces
* Do quick estimates: “If I double the distance, what happens to the force?”
* Know the difference between:
* Force between charges (Coulomb’s law)
* Electric field
* Electric potential energy

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====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">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</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]]
</div>
</div>

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

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

*[[Current]]

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Curved 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 field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</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">

====Circuitry Basics====
<div class="mw-collapsible-content">
*[[Understanding Fundamentals of Current, Voltage, and Resistance]]
</div>
</div>

<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">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

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

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[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]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</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]]
*[[Motors and Generators]]
*[[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">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====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]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<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">
*[[Classical Physics]]
</div>
</div>

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

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Twin Paradox]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<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]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

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

===Week 10===
<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 11===
<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 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Thermodynamics====
<div class="mw-collapsible-content">
*[[Maxwell Relations]]
*[[Brownian Motion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
*[[Radioactive Decay Processes]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Solid-State/Condensed Matter Physics====
<div class="mw-collapsible-content">
*[[What is Condensed Matter]]
*[[Crystalline Structures]]
*[[Electric-Band Structure]]
</div>
</div>

Right-Hand Rule

2025-04-23T03:29:51Z

Rsharma443: Added more applications and edited content

Claimed by Rithwik Sharma Spring 2025
==The Main Idea==

The Right-Hand Rule is an easy way to find the '''direction''' of a cross product interaction before doing the math. For any equation involving a cross product, the right hand rule is a valuable tool for finding the direction. There are two primary ways of using the right hand rule.

1) The first method is to use your entire right hand. Make shape of a high five with your right hand with your right hand, with your thumb sticking out perpendicular to the direction of your fingers. Align your hand with the first vector listed in the cross product. Then, curl your fingers toward the second vector listed in the cross product without moving your palm. You must rotate your hand to whatever orientation it requires for this to be possible, while keeping your thumb perpendicular to your fingers through the entire process. Your thumb will point in the direction of the cross product. In the example depicted below the cross product points "out" of the page, the same direction as the thumb.

[[File:RightHand1.png]]
[[File:RH2.png]]

2) The second method is extremely similar to the first. Start by making a thumbs up, and maintain your thumb extended in this way through the entire process. Extend your index (pointer) finger and align it with the first vector in the cross product. Extend your middle finger and align it with the second vector while keeping your ring and pinkie fingers closed. This will force you to orient your hand in such a way that your thumb will point in the direction of the cross product. This is demonstrated below.

[[File:Right hand rule cross product.svg|Right hand rule cross product]]

==A Mathematical Model==

The Right-Hand Rule is a technique for modeling the direction of a cross product:
:<math>\mathbf{u\times v}=(u_2v_3\mathbf{i}+u_3v_1\mathbf{j}+u_1v_2\mathbf{k})
-(u_3v_2\mathbf{i}+u_1v_3\mathbf{j}+u_2v_1\mathbf{k})
</math>

''The cross product can also be solved in the following form (using '''u''' and '''v'''):''
:<math>| \mathbf{u} \times \mathbf{v} | = | \mathbf{u} | | \mathbf{v} | \sin (\theta)</math>

===Cross Product: Alternate Method 1===

Alternate methods for computing a cross product exist, though this one is limited to cross products of 3 dimensions.

Structure the three components in a circle and assign a clockwise direction around this circle.

Crossing one component with another component that can be reached clockwise on on the next move around the circle yields a vector third direction.

This can be seen in the picture below.

[[File:CircleMethod2.png]]

In order to quickly solve a cross product using this alternate method, see the following example.

[[File:CircleCR3.png]]

Note: order matters in cross products. When crossing two vectors in the counter-clockwise direction the resulting third vector is negative.

===Cross Product: Alternate Method 2===
[[File:Wikicrossprod.png]]

===Cross Product: Alternate Method 3===

If you're personally more of a math person, and you have taken linear algebra or have done determinants before, cross products are essentially taking determinants of a 3x3 matrix.

1. For the first row, write down '''i, j, k'''. These are your directional components with '''"i"''' representing the +x direction, '''"j"''' the +y direction, and '''"k"''' the +z direction.

2. If you are crossing '''a x b''', write down the a components in the second row and b components in the third row corresponding to the x,y,z direction. If for example, ax is in the -x direction, simply make the value of ax negative.

3. Then take the determinant of the 3x3 matrix which is shown below. Don't forget that the second term ('''j''') must be negative.

[[File:Crossproductdet.png]]

==A Computational Model==

For a computational model, the Right-Hand Rule is just an easy way to determine the direction of the result of a cross product, but the model below allows you to change the two initial vectors, which the cross product will react to, and it will show that the right hand rule is true for any set of vectors that are not facing the same direction.
(Note: Just because you can determine the direction of a cross product using the RHR does '''NOT''' mean that every equation involving cross products will end up with that direction. Please make sure to account for any changes in sign, magnitude, or direction when solving cross product equations.

<html>
<iframe src="https://trinket.io/embed/glowscript/746a15552f" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>
<html>

==Examples==

===Magnetic Field for a Point Charge (Bio-Savart Law)===

The equation written in pink in the picture below is the Bio-Savart Rule for a single charged particle which will be later explained in further chapters. As you can see, there is a cross product within the equation, and it can be a little tricky finding the direction of the magnetic field.

Using the Right-Hand rule (alternative 2):
1. place your palm in the direction of velocity since it is velocity crossed rhat
2. curl your finger to the direction of rhat
3. Point your thumb up( perpendicular from your fingers) and this direction is the direction of your magnetic field, ''assuming that the charge is positive''.
If your charge is negative, then simply flip the direction of your thumb.

In the picture below, the direction of the magnetic field would be out of the page (+z) if the particle is positively charged. If the charge was an electron (negatively charged), then the direction of the magnetic field would be into the page (-z).

[[File:BioSavartUno1.png]]
[[File:Screen Shot 2018-11-25 at 23.13.22.png]]

===Magnetic Force on a Moving Particle===
:<math>\mathbf{F} = q\mathbf{v} \times \mathbf{B}</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The index finger points in the direction of the momentum vector qv.
# The middle finger points in the direction of the magnetic field vector B.
# The thumb points in the direction of magnetic force F.

For example, for a positively charged particle moving to the right, in a region where the magnetic field points up, the resultant force points out of the page (+z). If it was the same situation, but the particle was negatively charged, the you would flip the direction of your thumb, and the resultant force points into the page (-z).

===Magnetic Field made by a Current===

:<math> \mathbf{B} = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The thumb points in the direction of current I.
# The index finger points in the direction of the observation vector r.
# The middle finger points in the direction of the magnetic field vector B.

===Direction of Magnetic Field made by a Current===

The direction of curl of the magnetic field can be found using a modified right hand rule:
# The thumb points in the direction of conventional current.
# The curl of the fingers indicates the direction of magnetic field at each location surrounding the flow of current.

[[File:RHR_for_current.jpg]]

For example:
# In the image below, conventional current flows to the left (-x). By pointing your thumb in the -x direction and curling your fingers, the magnetic field curls in the y,z-plane, as shown.

[[File:RHR_current.jpg]]

===Force on a Current from a Magnetic Field===
:<math> \mathbf{F} = \mathbf{I} \times \mathbf{B}</math>

The direction of the cross product may be found by application of the right hand rule as follows:
# The index finger points in the direction of the current I.
# The middle finger points in the direction of the magnetic field vector B.
# The thumb points in the direction of magnetic force F.

For example, for a current moving into the page, in a region where the magnetic field points up, then the force is to the right of the current.

===Another Force on a Current from a Magnetic Field===
In the situation shown below, we have a current pointing downward or in the negative y direction and we have a magnetic field into the page or in the negative z direction. Instead of using the typical right hand rule, we can use easy cross product method below to find the direction of the force.

[[File:Lorentz1.png]]

===Hall Effect Example===

[[File:hall.png]]

In the above picture, you see that all the positive charges accumulated at the top and all the negative charges accumulated to the bottom. You know the direction the particles velocity and magnetic field. Can you find out the charge of the particle using the right hand rule?

In the picture, the particles are coming out of the negative terminal, so they are electrons. This can be verified by using the right hand rule. You curl your fingers from velocity vector to magnetic field vector to find the direction of magnetic force perpendicular. Your thumb is pointing up, but since these are negative charges, its opposite and you flip your hand and you find that the direction of the magnetic force is actually pointing down. Therefore it makes sense that the electrons would accumulate at the bottom since its magnetic force is pushing them towards there.

==Applications in Modern Technology==

The right-hand rule isn’t just a physics classroom trick—it underpins the functionality of numerous modern technologies. For example, electric motors and generators operate directly based on the principles of electromagnetism, where magnetic fields and currents interact to produce motion or induce voltage. In a DC motor, the current flows through coils situated in a magnetic field. The force exerted on these coils due to the magnetic field (as determined by the right-hand rule) causes them to rotate, converting electrical energy into mechanical work. Conversely, in a generator, mechanical rotation in a magnetic field generates a current, again aligning with the right-hand rule but in reverse.

Another major application is in the field of particle accelerators and mass spectrometers, where charged particles are manipulated using magnetic fields. Engineers and physicists use the right-hand rule to design magnetic steering systems that control the trajectory of high-speed electrons, protons, or ions. Accurate directional control is essential, as even the smallest miscalculation in the force vector can cause particles to crash into containment walls or skew the results of delicate experiments.

Additionally, magnetic resonance imaging (MRI) systems use rapidly changing magnetic fields to align and detect the spin of atomic nuclei in the human body. The right-hand rule helps explain how the magnetic fields interact with current-carrying wires in the machine’s gradient coils to produce spatially varying fields. These interactions are critical for encoding location information in the resulting medical images, showcasing how a basic vector rule plays a role in saving lives.

The right-hand rule is also crucial in aerospace and satellite engineering, where magnetic torquers are used for attitude control of satellites. These torquers generate magnetic dipoles that interact with Earth’s magnetic field to produce torque, allowing engineers to rotate or stabilize satellites without using fuel. To predict and control these rotational effects accurately, the right-hand rule helps determine the direction of torque from the interaction between the satellite’s internal current loops and Earth’s geomagnetic field. This method of non-propulsive control is lightweight, reliable, and energy-efficient, making it ideal for long-duration missions in low Earth orbit.

==Connectedness==

1. How is the topic connected to something you are interested in?

It's honestly a valuable tool in determining the direction of cross-products which allows me to see if my math is correct. For example, to figure out the direction of the conventional current that flows in a wire whose magnetic field changes the direction of a compass, I would have the use the right-hand rule to help me out.

If a charged particle is moving at a certain speed and is under a magnetic field, the right-hand rule can be used to determine the force the particle will experience.

2. How is it connected to your major?

As a computer engineering major, it is very relevant in my physics class, and although we don't see the right hand rule in action first-hand, I know it plays a critical role in what we do when designing circuits and can be used to explain things at a molecular level.

3. Is there an industrial application?

Using sails for a boat deals with cross-product because when the wind blows, the sails experience angular momentum '''L = I x w'''

==History==
[[File:John Ambrose Fleming 1890.png|thumb|left| John Ambrose Fleming 1890]]
John Ambrose Fleming is credited with devising the right-hand rule. He was a professor at the University College, London where he was liked by many of his students. Fleming devised the right hand rule (though Fleming's original version used the left hand) in order to make relationships between current, its magnetic field, and the electromotive force easier to visualize and understand.

Though he was best known for his right-hand rule in which he connected the observation vector, magnetic field, and current, he also had a left-hand rule as well which he used for motors. It connected force, magnetic field, and current.

[[File:LeftHandOutline.png|thumb|Fleming's original rule]]

==See Also==

===External Links===

#https://www.khanacademy.org/test-prep/mcat/physical-processes/magnetism-mcat/a/using-the-right-hand-rule
#https://ocw.mit.edu/courses/physics/8-02t-electricity-and-magnetism-spring-2005/lecture-notes/prs_w06d1.pdf
#http://physics.bu.edu/~duffy/semester2/d12_RHR_practice.html

==References==

#https://en.wikipedia.org/wiki/Right-hand_rule
#https://en.wikipedia.org/wiki/Magnetic_field
#https://nationalmaglab.org/education/magnet-academy/history-of-electricity-magnetism/pioneers/john-ambrose-fleming

[[Category:Fields]]