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| * A page to keep track of all the physics [[Constants]] | | * A page to keep track of all the physics [[Constants]] |
| * A listing of [[Notable Scientist]] with links to their individual pages | | * A listing of [[Notable Scientist]] with links to their individual pages |
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| <div style="float:left; width:30%; padding:1%;"> | | <div style="float:left; width:30%; padding:1%;"> |
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| ===Week 7=== | | ===Week 7=== |
| <div class="toccolours mw-collapsible mw-collapsed"> | | <div class="toccolours mw-collapsible mw-collapsed"> |
| ====Jeet Bhatkar==== | | ====Identifying Forces==== |
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| ====Energy Principle====
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| 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.
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| <div class="mw-collapsible-content"> | | <div class="mw-collapsible-content"> |
|
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| *[[Kinetic Energy]] | | *[[Kinetic Energy]] |
| Kinetic energy is the energy an object possesses due to its motion.
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| *[[Work/Energy]] | | *[[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.
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| *[[The Energy Principle]] | | *[[The Energy Principle]] |
| Work and energy are closely related concepts. Work (
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| 𝑊) done on an object is defined as the force (
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| 𝐹) applied to the object multiplied by the displacement (
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| 𝑑) of the object in the direction of the force:
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| 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.
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| *[[Conservation of Energy]] | | *[[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.
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| </div> | | </div> |
| </div> | | </div> |
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| *[[Predicting the Position of a Rotating System]] | | *[[Predicting the Position of a Rotating System]] |
| *[[The Moments of Inertia]] | | *[[The Moments of Inertia]] |
| | *[[Parallel axis theorem]] |
| *[[Right Hand Rule]] | | *[[Right Hand Rule]] |
| </div> | | </div> |
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| ====Electric field==== | | ====Electric field==== |
| <div class="mw-collapsible-content"> | | <div class="mw-collapsible-content"> |
| RITHWIK SHARMA FALL 2025
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| *[[Electric Field]] | | *[[Electric Field]] |
| An electric field shows how a charged object pushes or pulls on other charges around it. The field points in the direction a positive charge would move, and its strength depends on how much charge is creating it and how far away you are.
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| *[[Electric Field and Electric Potential]] | | *[[Electric Field and Electric Potential]] |
| Electric potential describes how much energy per charge is stored at a point in space. The electric field tells you how that potential changes from one point to another. Steeper changes in potential create stronger electric fields.
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| </div> | | </div> |
| </div> | | </div> |
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| <div class="toccolours mw-collapsible mw-collapsed"> | | <div class="toccolours mw-collapsible mw-collapsed"> |
|
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| == Electric force ==
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| '''Jeet Bhatkar – Fall 2025'''
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|
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| == Big Idea ==
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| Electric force is the interaction between objects that have electric charge. It is:
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|
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| * '''Long-range''': acts even when charges do not touch
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| * '''Vector-valued''': has magnitude and direction
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| * '''Superposable''': forces from many charges add as vectors
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|
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| 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.
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|
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| == Key Equations ==
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|
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| '''Coulomb’s Law (magnitude)'''
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| :[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]
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|
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| * [math]\displaystyle{F}[/math] = magnitude of the electric force
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| * [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
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| * [math]\displaystyle{q_1, q_2}[/math] = charges (C)
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| * [math]\displaystyle{r}[/math] = separation between the charges (m)
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|
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| '''Coulomb’s Law (vector form)'''
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| :[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]
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|
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| * [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
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| * [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2
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|
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| '''Relation to Electric Field'''
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| :[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]
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|
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| 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.
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|
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| == Conceptual Picture ==
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|
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| '''Sign of charges'''
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| * Like charges (both positive or both negative) → '''repel'''
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| * Unlike charges (one positive, one negative) → '''attract'''
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|
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| '''Distance dependence'''
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| * Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.
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|
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| '''Superposition principle'''
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| If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge:
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| [math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].
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|
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| '''Electric vs. gravitational force'''
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| * Both follow inverse-square laws
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| * Gravity is always attractive; electric force can be attractive or repulsive
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| * Electric forces are usually much stronger at the particle scale
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|
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| == Worked Example 1: Two Point Charges on a Line ==
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|
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| '''Problem.'''
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| Two charges are placed on the x-axis:
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|
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| * [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
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| * [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]
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|
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| What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?
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|
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| '''Solution (outline).'''
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|
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| # Distance between charges:
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| [math]\displaystyle{ r = 0.40\ \text{m} }[/math].
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|
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| # Magnitude using Coulomb’s law:
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| [math]\displaystyle{
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| F = k \dfrac{|q_1 q_2|}{r^2}
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| = (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2}
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| }[/math]
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|
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| # Sign and direction:
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| * [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is '''attractive'''
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| * On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
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| * Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the '''−x''' direction
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|
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| 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].
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|
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| == Worked Example 2: Superposition with Three Charges ==
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|
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| '''Problem.'''
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| 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?
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|
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| '''Idea (no full algebra).'''
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|
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| * Each of the other two charges exerts a force of magnitude
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| [math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]
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| * The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
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| * Use vector addition:
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| * Add components along the symmetry axis
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| * Perpendicular components cancel by symmetry
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|
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| This shows how symmetry plus superposition simplify the vector addition.
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|
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| == Computational Model (GlowScript) ==
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|
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| Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.
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|
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| You can:
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| * Paste this into a new GlowScript Trinket (Python / VPython),
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| * Get the embed code from Trinket,
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| * Embed that code into this page so it runs directly here.
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|
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| <syntaxhighlight lang="python">
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| from vpython import *
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|
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| # constant
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| k = 8.99e9 # N·m^2/C^2
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|
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| # scene setup
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| scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"
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|
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| # charges (positions in meters, charges in coulombs)
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| q1 = 2e-6 # C (blue, fixed)
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| q2 = -3e-6 # C (red, movable)
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|
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| charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue)
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| charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)
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|
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| # arrow to show force on q2 due to q1
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| F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))
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|
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| def electric_force(q1, q2, r1, r2):
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| r_vec = r2 - r1
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| r = mag(r_vec)
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| if r == 0:
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| return vector(0, 0, 0)
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| F_mag = k * q1 * q2 / r**2
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| return F_mag * norm(r_vec)
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|
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| dragging = False
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|
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| def down():
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| global dragging
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| if scene.mouse.pick is charge2:
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| dragging = True
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|
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| def up():
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| global dragging
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| dragging = False
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|
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| scene.bind("mousedown", lambda evt: down())
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| scene.bind("mouseup", lambda evt: up())
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|
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| while True:
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| rate(60)
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|
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| if dragging:
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| # move the red charge with the mouse in the x-y plane
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| m = scene.mouse.pos
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| charge2.pos = vector(m.x, m.y, 0)
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|
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| F = electric_force(q1, q2, charge1.pos, charge2.pos)
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|
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| # update arrow to show force on q2
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| F_arrow.pos = charge2.pos
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| # scale arrow length for visibility (purely visual)
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| F_arrow.axis = F * 1e7
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| </syntaxhighlight>
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|
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| You can extend this model to include more charges or show the net force on a test charge at different locations.
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|
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| == Common Mistakes and How to Avoid Them ==
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|
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| * '''Forgetting that force is a vector.'''
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| Always draw a diagram and keep track of directions. Use components in 2D/3D.
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| * '''Dropping the absolute value in the magnitude formula.'''
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| [math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.
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| * '''Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].'''
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| The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].
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| * '''Using wrong units.'''
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| Convert microcoulombs to coulombs, centimeters to meters, etc.
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| [math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].
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| * '''Trying to memorize instead of understand.'''
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| Focus on inverse-square behavior, sign of charges, and superposition.
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|
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| == Connections to Other Topics ==
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|
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| * '''Electric Field''' – Electric force per unit charge is the electric field:
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| [math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].
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| * '''Potential Energy and Electric Potential''' – Work done by electric forces leads to electric potential energy and voltage.
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| * '''Lorentz Force''' – The full force on a moving charge also includes magnetic fields:
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| [math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].
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| This page focuses on the electric part.
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|
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| == Practice Problems ==
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|
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| You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.
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|
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| # 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.
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| * (a) Find the magnitude of the force on each charge.
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| * (b) Is the force attractive or repulsive? Explain.
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|
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| # 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].
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| * Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).
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| * Verify that Newton’s third law holds (forces are equal and opposite).
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|
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| # Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].
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| * Find the net force on one of the corner charges.
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| * Use symmetry to simplify the vector addition.
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|
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| # 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.
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| * (a) What is the electric field at that point (magnitude and direction)?
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| * (b) If the charge were positive instead, what would the force direction be?
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|
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| == What to Review Before an Exam ==
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|
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| * Determine force direction from a diagram, not just from algebra
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| * Practice vector addition of multiple forces
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| * Do quick estimates: “If I double the distance, what happens to the force?”
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| * Know the difference between:
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| * Force between charges (Coulomb’s law)
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| * Electric field
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| * Electric potential energy
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|
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|
| ====Electric field of a point particle==== | | ====Electric field of a point particle==== |
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| *[[Electric Potential]] | | *[[Electric Potential]] |
| *[[Path Independence of Electric Potential]] | | *[[Path Independence of Electric Potential]] |
| *[[Potential Difference Path Independence, claimed by Aditya Mohile]] | | *[[Potential Difference Path Independence]] |
| *[[Potential Difference in a Uniform Field]] | | *[[Potential Difference in a Uniform Field]] |
| *[[Potential Difference of Point Charge in a Non-Uniform Field]] | | *[[Potential Difference of Point Charge in a Non-Uniform Field]] |
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| </div> | | </div> |
| <div class="toccolours mw-collapsible mw-collapsed"> | | <div class="toccolours mw-collapsible mw-collapsed"> |
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| ====Sign of a potential difference==== | | ====Sign of a potential difference==== |
| <div class="mw-collapsible-content"> | | <div class="mw-collapsible-content"> |
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| <div class="mw-collapsible-content"> | | <div class="mw-collapsible-content"> |
| *[[Moving Point Charge]] | | *[[Moving Point Charge]] |
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| 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.
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| *[[Current]] | | *[[Current]] |
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| 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.
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| </div> | | </div> |
| </div> | | </div> |
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| *[[Loop Rule]] | | *[[Loop Rule]] |
| *[[Node Rule]] | | *[[Node Rule]] |
| | *[[Kirchoff's_Laws]] |
| </div> | | </div> |
| </div> | | </div> |