AP PHYSICS 2 — physicsMedium3 min read

Magnetism & Electromagnetic Induction

AP Physics 2 study guide for magnetism: magnetic fields, forces on moving charges, current-carrying wires, Faraday's law, and Lenz's law.

Tutor AI Team2026-02-26T00:10:28.828Z

# Magnetism & Electromagnetic Induction — AP Physics 2

Magnetism and electromagnetic induction link electric and magnetic phenomena. AP Physics 2 covers magnetic fields, forces on charges and currents, and the induction of EMF by changing magnetic flux. These concepts are fundamental to generators, transformers, and much of modern technology.

Key Concepts

Magnetic Fields

Produced by moving charges, current-carrying wires, and permanent magnets.
Field lines exit from the north pole and enter the south pole.
Unit: tesla (T). $1\ \text{T} = 1\ \text{kg/(A·s}^2\text{)}$ .

Force on a Moving Charge

$F = qvB\sin\theta$

Direction given by the right-hand rule.
Force is perpendicular to both $\vec{v}$ and $\vec{B}$ .
A charge moving parallel to $\vec{B}$ feels no force.
A charged particle in a uniform $\vec{B}$ (perpendicular entry) moves in a circle: $r = \frac{mv}{qB}$

Force on a Current-Carrying Wire

$F = BIL\sin\theta$ where $L$ is the length of wire in the field.

Magnetic Field from a Long Straight Wire

$B = \frac{\mu_0 I}{2\pi r}$ where $\mu_0 = 4\pi \times 10^{-7}\ \text{T·m/A}$ .

Magnetic Flux

$\Phi_B = BA\cos\theta$ Unit: weber (Wb).

Faraday's Law of Induction

$\mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t}$

An EMF is induced whenever the magnetic flux through a loop changes.

Lenz's Law

The induced current flows in a direction that opposes the change in flux that caused it.

Worked Example

Problem: An electron ( $q = 1.6 \times 10^{-19}\ \text{C}$ , $m = 9.11 \times 10^{-31}\ \text{kg}$ ) enters a uniform $0.5\ \text{T}$ magnetic field perpendicular to its velocity of $2 \times 10^6\ \text{m/s}$ . What is the radius of its circular path?

Solution:

$r = \frac{mv}{qB} = \frac{(9.11 \times 10^{-31})(2 \times 10^6)}{(1.6 \times 10^{-19})(0.5)}$ $r = \frac{1.822 \times 10^{-24}}{8 \times 10^{-20}} = 2.28 \times 10^{-5}\ \text{m} \approx 0.023\ \text{mm}$

Practice Questions

1. A proton moves at $3 \times 10^5\ \text{m/s}$ perpendicular to a $0.2\ \text{T}$ field. What force does it experience?

$F = qvB = (1.6 \times 10^{-19})(3 \times 10^5)(0.2) = 9.6 \times 10^{-15}\ \text{N}$ .

2. A $2\ \text{m}$ wire carrying $5\ \text{A}$ is perpendicular to a $0.3\ \text{T}$ field. What force acts on it?

$F = BIL = 0.3(5)(2) = 3\ \text{N}$ .

3. A circular loop of area $0.05\ \text{m}^2$ is in a field that changes from $0.4\ \text{T}$ to $0$ in $0.1\ \text{s}$ . What is the induced EMF?

$\mathcal{E} = |\Delta\Phi/\Delta t| = |0.05(0 - 0.4)|/0.1 = 0.02/0.1 = 0.2\ \text{V}$ .

4. A bar magnet is pushed toward a conducting loop. In what direction does the induced current flow (relative to the approaching north pole)?

By Lenz's law, the induced current creates a field opposing the increasing flux, so it flows to create a north pole facing the incoming magnet (counterclockwise when viewed from the magnet's side).

Want to check your answers and get step-by-step solutions?

Summary

Magnetic force on a charge: $F = qvB\sin\theta$ (perpendicular to $\vec{v}$ and $\vec{B}$ ).
A charged particle in a perpendicular field moves in a circle of radius $r = mv/(qB)$ .
Faraday's law: changing magnetic flux induces an EMF.
Lenz's law: the induced current opposes the change in flux.

Tags:

#ap#physics#magnetism

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