Point Charges - Fields & Potentials

Abigail Wright

7 min read

Next Topic - Gauss' Law

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Study Guide Overview

This study guide covers work and electric potential energy, including the relationship between work done by electric forces and changes in potential energy. It also explains electric potential (voltage), its relationship to potential energy, and how to calculate it for point charges and multiple charges. Equipotential lines and their relationship to electric field lines are discussed. Finally, the guide provides practice questions and exam tips covering conceptual, calculation, and graphical questions related to these topics.

#AP Physics C: E&M - Electric Fields & Potential: Your Night-Before Review ⚡

Hey there, future physicist! Let's get you prepped and confident for your exam. This guide is designed to be your go-to resource for a quick, effective review of electric fields and potential. Let's dive in!

#1. Work and Electric Potential Energy

#Work Done by Electric Forces

Remember that work is done when moving charges in an electric field. It's all about overcoming the electric force. 🏋️
Key Formula: $W = \int F \cdot dr$ or $W = Fd\cos(\theta)$ where W is work, F is the force, and d is the displacement.
For electric forces, this translates to changes in electric potential energy ( $U_e$ ).

Key Concept

Crucial Insight: Work done is equal to the change in electric potential energy: $W = -\Delta U_e$ . The negative sign indicates that work done by the field decreases potential energy, and work done against the field increases it.

#Electric Potential Energy ( $U_e$ )

Definition: The energy a charge has due to its position in an electric field.
Formula (Point Charges): $\Delta U_e = \frac{k q_1 q_2}{r}$ where k is Coulomb's constant, q are the charges, and r is the distance between them.
Important Note: $U_e$ is a scalar quantity. No direction, just magnitude!
Multiple Charges: The total $U_e$ is the sum of all individual $U_e$ values, considering positive and negative signs.

# $U_e$ and Electric Field Strength

$U_e$ can also be expressed using the electric field (E) and displacement (d):
Connection: Remember that $Ed = \Delta V$ (change in electric potential), so $\Delta U_e = q...

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Previous Topic - Electric Fields & Electric Potential Next Topic - Gauss' Law

Question 1 of 11

If an electric field does positive work on a charge, what happens to the electric potential energy of that charge? 🤔

The potential energy increases

The potential energy decreases

The potential energy remains constant

The potential energy becomes zero