#AP Physics C: E&M - Electric Potential Energy Study Guide

Hey there! Let's get you prepped and confident for your AP Physics C: E&M exam. We're diving into electric potential energy, a key concept that shows up everywhere on the test. Think of this as your ultimate cheat sheet for tonight.

#Electric Potential Energy: The Basics

Electric potential energy is all about the energy stored in a system of charged particles because of their electric field interactions. It's like the potential a stretched spring has to do work. The closer like charges are, the more potential energy they have, and the opposite is true for opposite charges.

• Definition: Energy stored in a system of charges due to their positions and interactions.

• Key Idea: Work is required to bring like charges together and to separate opposite charges. This work is stored as potential energy.

#Work and Potential Energy

• Work-Energy Connection: The work done by an external force to move charges into their current arrangement is equal to the electric potential energy stored in the system.

• Analogy: Imagine lifting a book against gravity. You do work, and the book gains gravitational potential energy. Similarly, when you move charges around, you're doing work, and the system gains electric potential energy.

• Release: When charges move to a lower potential energy configuration, this stored energy is released (like a book falling).

#Calculating Electric Potential Energy

• Formula: The electric potential energy ($U_E$) between two point charges is given by:

$$U_{E} = k \frac{q_1 q_2}{r}$$

Where: - $U_E$ is the electric potential energy (in Joules, J) - $q_1$ and $q_2$ are the magnitudes of the charges (in Coulombs, C) - $r$ is the distance between the charges (in meters, m) - $k$ is Coulomb's constant (8.99 \times 10^9 \frac{\text{N} \cdot \text{m}^2}{\text{C}^2})

• Inverse Relationship: Notice the $\frac{1}{r}$ term. This means that: - Potential energy decreases as the distance between the charges increases. - Doubling the distance halves the potential energy.

• Sign Matters: - Like charges (both positive or both negative) have a ...