Physics Book - User contributions [en]

Magnetic Field of a Curved Wire

2025-12-01T04:34:48Z

Jeet2004: Created page with "== Creating Magnetic Field of a Curved Wire == '''Jeet Bhatkar – Fall 2025''' == Big Idea == An electric current in a wire creates a magnetic field that curls around the wire. For a curved wire, each tiny piece of the wire contributes a small magnetic field. The total field is found by adding (integrating) all these contributions. For arcs of a circle, this leads to simple and very useful formulas. == Key Equations == '''Biot–Savart Law (for a small piece of wire..."

== Creating Magnetic Field of a Curved Wire ==
'''Jeet Bhatkar – Fall 2025'''

== Big Idea ==
An electric current in a wire creates a magnetic field that curls around the wire.

For a curved wire, each tiny piece of the wire contributes a small magnetic field. The total field is found by adding (integrating) all these contributions. For arcs of a circle, this leads to simple and very useful formulas.

== Key Equations ==

'''Biot–Savart Law (for a small piece of wire)'''
:<math>d\vec{B} = \frac{\mu_0}{4\pi}\,\frac{I\, d\vec{\ell} \times \hat{r}}{r^2}</math>

* <math>\mu_0</math> = permeability of free space
* <math>I</math> = current (A)
* <math>d\vec{\ell}</math> = tiny vector along the wire (direction of current)
* <math>\hat{r}</math> = unit vector from the wire element to the field point
* <math>r</math> = distance from the wire element to the field point

'''Magnetic field at the center of a circular arc'''

For a wire shaped as a circular arc of radius <math>R</math> and angle <math>\theta</math> (in radians), carrying current <math>I</math>:

:<math>B = \frac{\mu_0 I}{4\pi R}\,\theta</math>

Direction: given by the right–hand rule (thumb along current, fingers curl in direction of <math>\vec{B}</math> through the center).

Special cases:

* Full circle: <math>\theta = 2\pi</math>, field at the center is
<math>B = \dfrac{\mu_0 I}{2R}</math>
* Semicircle: <math>\theta = \pi</math>, field at the center is
<math>B = \dfrac{\mu_0 I}{4R}</math>

== Conceptual Picture ==
* Magnetic field lines form closed loops around the current.
* For a circular arc, field lines near the center look like circles centered on the arc’s center.
* The more wire around the center (larger <math>\theta</math>) or the larger the current <math>I</math>, the stronger the field there.
* Increasing the radius <math>R</math> spreads the current farther away, so the field at the center gets weaker: <math>B \propto 1/R</math>.

Use the right–hand rule: point your thumb along the current; your fingers curl in the direction of the magnetic field.

== Worked Example: Field at the Center of a Semicircular Wire ==

'''Problem.'''
A thin wire is bent into a semicircle of radius <math>R = 5.0\,\text{cm}</math>. A current of <math>I = 3.0\,\text{A}</math> flows through the wire. Find the magnitude and direction of the magnetic field at the center of the semicircle.

'''Solution.'''

The semicircle is a circular arc with <math>\theta = \pi</math>. Use the arc formula:

:<math>
B = \frac{\mu_0 I}{4\pi R}\,\theta
= \frac{\mu_0 I}{4\pi R}\,\pi
= \frac{\mu_0 I}{4R}
</math>

Convert <math>R</math> to meters:

:<math>R = 5.0\,\text{cm} = 0.050\,\text{m}</math>

Then:

:<math>
B = \frac{(4\pi \times 10^{-7}\,\text{T·m/A})(3.0\,\text{A})}{4(0.050\,\text{m})}
\approx 1.9 \times 10^{-5}\,\text{T}
</math>

Direction: use the right–hand rule for the current around the semicircle.

* If current flows counterclockwise as seen from above, <math>\vec{B}</math> at the center points out of the page.
* If current flows clockwise, <math>\vec{B}</math> points into the page.

== Computational Model (GlowScript) ==
This GlowScript model approximates a circular arc by many small straight segments and uses the Biot–Savart law to compute the magnetic field at the center.

<syntaxhighlight lang="python">
from vpython import *
import numpy as np

# constants
mu0 = 4*pi*1e-7 # T·m/A
I = 3.0 # current (A)
R = 0.1 # radius of arc (m)
theta_total = pi # total angle of arc (radians), e.g. pi for semicircle

N = 200 # number of segments

scene.caption = "Magnetic field at the center of a curved wire (arc)\n"
scene.width = 700
scene.height = 400

# center where we calculate B
r_center = vector(0, 0, 0)

# draw the wire as small cylinders along an arc in the x–y plane
wire_segments = []
angles = np.linspace(-theta_total/2, theta_total/2, N)

for i in range(N - 1):
a1 = angles[i]
a2 = angles[i + 1]
p1 = vector(R*cos(a1), R*sin(a1), 0)
p2 = vector(R*cos(a2), R*sin(a2), 0)
seg = cylinder(pos=p1, axis=(p2 - p1), radius=0.003, color=color.orange)
wire_segments.append(seg)

# arrow to show magnetic field at the center
B_arrow = arrow(pos=r_center, axis=vector(0, 0, 0), color=color.cyan)

def compute_B_center():
B = vector(0, 0, 0)
for seg in wire_segments:
dl = seg.axis # direction of current element
r_mid = seg.pos + 0.5*seg.axis # midpoint of the segment
r_vec = r_center - r_mid
r = mag(r_vec)
if r == 0:
continue
dB = (mu0*I/(4*pi)) * cross(dl, r_vec) / r**3
B += dB
return B

B = compute_B_center()
B_arrow.axis = B * 5e5 # scale so we can see the arrow

scene.append_to_caption(f"Approximate |B| at center = {mag(B):.3e} T\n")
</syntaxhighlight>

You can experiment by changing <math>I</math> (current), <math>R</math> (radius), and <math>\theta_\text{total}</math> (total angle in radians).

== Common Mistakes ==
* '''Using degrees instead of radians in the arc formula.'''
The formula <math>B = \dfrac{\mu_0 I}{4\pi R}\,\theta</math> assumes <math>\theta</math> is in radians.
* '''Forgetting that the arc formula is for the field at the center of the circle only.'''
* '''Getting the right–hand rule backwards.'''
Thumb along current; curled fingers show the direction of <math>\vec{B}</math>.
* '''Ignoring contributions from straight segments''' in mixed “straight + curved” wire problems.

== Practice Problems ==
# A wire is bent into a quarter–circle of radius <math>R</math> carrying current <math>I</math>.
* (a) Find the magnitude of the magnetic field at the center of the circle.
* (b) If the quarter–circle is completed to a full circle with the same current, by what factor does <math>B</math> change?

# A wire consists of a semicircle of radius <math>R</math> connected to two long straight segments that extend radially outward from the ends of the semicircle.
* Find the direction of the net magnetic field at the center.
* Which part (arc or straight segments) contributes most to the magnitude? Explain qualitatively.

# A circular loop of radius <math>R</math> carries current <math>I</math>.
* (a) Find <math>B</math> at the center.
* (b) If only half of the loop remained (a semicircle), what would <math>B</math> be at the center?

# You are given a choice of two wires to create a magnetic field at a point:
(1) a small circular loop of radius <math>R</math> with current <math>I</math>, or
(2) a larger circular loop of radius <math>2R</math> with the same current.
* Which produces the larger <math>B</math> at its center? Show your reasoning.

== Copyright and Image Ideas ==
* Draw your own diagram of a curved wire (arc) with the current direction and the magnetic field at the center indicated by an arrow into or out of the page.
* Draw a full circular loop with field lines near the center.

After you create the images, upload them and insert them with:

[[File:Curved_wire_Bfield.png|thumb|Magnetic field at the center of a current-carrying arc.]]

[[File:Circular_loop_Bfield.png|thumb|Magnetic field at the center of a current in a circular loop.]]

File:Circular loop Bfield.png

2025-12-01T04:34:27Z

Jeet2004:

File:Curved wire Bfield.png

2025-12-01T04:33:42Z

Jeet2004:

Main Page

2025-12-01T04:17:36Z

Jeet2004: /* Copyright and Image Ideas */

__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]]
*[[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

2025-12-01T04:13:25Z

Jeet2004: /* Copyright and Image Ideas */

__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]]
*[[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?

== Copyright and Image Ideas ==

[[File:Phys2image.png|200px|thumb|left|Caption]]

== 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

2025-12-01T04:12:43Z

Jeet2004: /* Copyright and Image Ideas */

__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]]
*[[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?

== Copyright and Image Ideas ==

[[File:phys2image.png|200px|thumb|left|Caption]]

== 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>

File:Phys2image.png

2025-12-01T04:10:39Z

Jeet2004:

Main Page

2025-12-01T04:09:13Z

Jeet2004: /* Electric force */

__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]]
*[[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?

== Copyright and Image Ideas ==

== 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

2024-04-23T19:06:14Z

Jeet2004: /* Energy Principle */

__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]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

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

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

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

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

====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]]
*[[Current]]
</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">
*[[Kirchoff's Laws]]
</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]]
*[[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">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</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>

Main Page

2024-04-23T19:04:36Z

Jeet2004: /* Energy Principle */

__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">
====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">

*[[Energy of a Single Particle]]

*[[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
W) done on an object is defined as the force (
𝐹
F) applied to the object multiplied by the displacement (
𝑑
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====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

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

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

====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]]
*[[Current]]
</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">
*[[Kirchoff's Laws]]
</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]]
*[[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">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</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>