#AP Physics C: E&M - Ampère's Law & Maxwell's Equations Study Guide

Hey there, future physics pro! Let's get you prepped and confident for the AP exam. This guide is designed to be your go-to resource, especially the night before the test. We'll break down complex topics into easy-to-digest pieces, focusing on what's most important. Let's dive in!

#1. Magnetic Fields from Moving Charges

#1.1. Ampère's Law and Magnetic Fields

• Ampère's Law: Relates the magnetic field strength to the current passing through a closed loop (Amperian loop). 🔁

• Amperian Loop: An imaginary closed path used to apply Ampère's law. It's like a 'magnetic field measuring tape' that you place strategically.

  

  Caption: An Amperian loop encircling a current-carrying wire. The direction of the magnetic field is indicated by the circular arrows.

• Magnetic Field around a Long, Straight Wire:

  • Formula: $$B_{\text {wire }}=\frac{\mu_{0}}{2 \pi} \frac{I}{r}$$
  • $B_{\text {wire }}$: Magnetic field strength at a distance r from the wire.
  • $\mu_{0}$: Permeability of free space (a constant).
  • I: Current flowing through the wire.

• Magnetic Field Inside a Long Solenoid:

  • Formula: $$B_{\text {sol }}=\mu_{0} n I$$
  • $B_{\text {sol }}$: Magnetic field strength inside the solenoid.
  • n: Number of turns per unit length of the solenoid.

#1.2. Amperian Loops

• Concept: An Amperian loop is a closed path that encircles a current-carrying conductor. It's the path you use to apply Ampère's law.
• Purpose: It enables us to determine the...