---
title: "AP Physics 2 12.2: Magnetism and Moving Charges"
description: "Learn how moving charges create magnetic fields and how the force FB = qvB sinθ and right-hand rule apply on the AP Physics 2 exam."
canonical: "https://fiveable.me/ap-physics-2-revised/unit-12/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5"
type: "study-guide"
subject: "AP Physics 2"
unit: "Unit 12 – Magnetism and Electromagnetism"
lastUpdated: "2026-06-09"
---

# AP Physics 2 12.2: Magnetism and Moving Charges

## Summary

Learn how moving charges create magnetic fields and how the force FB = qvB sinθ and right-hand rule apply on the AP Physics 2 exam.

## Guide

A moving charge creates a magnetic field, and an external magnetic field exerts a force on a charge moving through it. The [magnetic force](/ap-physics-2-revised/key-terms/magnetic-force "fv-autolink") has magnitude $F_B = qvB\sin\theta$, points perpendicular to both [velocity](/ap-physics-2-revised/key-terms/velocity "fv-autolink") and field, and follows the right-hand rule for direction.

## Why This Matters for the AP Physics 2 Exam

Magnetism and moving charges is part of [Unit 12](/ap-physics-2-revised/unit-12 "fv-autolink"), which carries about 12 to 15 percent of the exam. This topic shows up in both multiple-choice and free-response questions, where you may need to predict how the magnetic force changes when you adjust charge, speed, field strength, or angle. On free-response items, you have to explain your reasoning step by step. Saying "the force points right because of the right-hand rule" does not support a stronger score. You need to connect the equation or principle to a clear explanation of why the force points where it does.

## Key Takeaways

- A single moving charge produces a magnetic field that is stronger at higher speeds, weaker farther away, and depends on the angle between the velocity and the position vector to the point.
- The magnetic force on a moving charge is $F_B = qvB\sin\theta$, so it depends on charge, speed, field strength, and angle.
- The magnetic force is always perpendicular to both the velocity and the magnetic field, and its direction comes from the right-hand rule (reverse it for negative charges).
- Force is zero when velocity is parallel to the field ($\theta = 0^\circ$ or $180^\circ$) and maximum when velocity is perpendicular ($\theta = 90^\circ$).
- When both electric and magnetic fields are present, the charge feels independent forces that you add as vectors.
- The [Hall effect](/ap-physics-2-revised/key-terms/hall-effect "fv-autolink") is the [potential difference](/ap-physics-2-revised/key-terms/electric-potential-difference "fv-autolink") created across a conductor when a magnetic field pushes its moving charges sideways.

## Magnetic Field Produced by Moving Charges

A charged particle that moves through space creates a magnetic field around it. This is one of the core links between electricity and magnetism.

For [AP Physics 2](/ap-physics-2-revised "fv-autolink"), describe this relationship qualitatively. The magnetic field from a single moving charge:

- Gets stronger when the charge moves faster.
- Gets weaker farther from the charge.
- Depends on the angle between the velocity vector and the position vector pointing from the charge to your point of interest.

The field is zero when those two vectors are parallel and greatest when they are perpendicular. At any chosen point, the field direction is perpendicular to both the velocity and the position vector, and you find that direction with the right-hand rule for a [positive charge](/ap-physics-2-revised/unit-10/3-electric-fields/study-guide/I5lSNgudkyVNrR1L "fv-autolink"). For a [negative charge](/ap-physics-2-revised/key-terms/negative-charge "fv-autolink"), the direction is reversed.

## Force Exerted on Moving Charges by Magnetic Fields

### Magnetic Interactions Between Moving Charges

Moving charges interact with each other through magnetic forces. This interaction is behind many electromagnetic phenomena.

- When two charges move, each creates a magnetic field that exerts a force on the other.
- These magnetic interactions depend on the motion of the charges.
- Unlike electric forces, which act along the line connecting two charges, magnetic forces act perpendicular to the motion.

### Force on a Charge Moving Through a Field

When a charged particle moves through a magnetic field, it feels a force that depends on several quantities. The magnitude is:

$$F_B = qvB\sin\theta$$

Where:
- $F_B$ is the magnetic force
- $q$ is the charge of the particle
- $v$ is the speed of the particle
- $B$ is the magnetic field strength
- $\theta$ is the angle between the velocity and [magnetic field vectors](/ap-physics-2-revised/unit-12/3-magnetism-and-current-carrying-wires/study-guide/TzaJHQDjTp5y8iuQ "fv-autolink")

The direction of this force is always perpendicular to both the magnetic field and the charge's velocity.

Use the right-hand rule to find the direction:

1. Point your fingers in the direction of the velocity $v$.
2. Curl them toward the magnetic field $B$.
3. Your thumb points in the direction of the force $F$ for a positive charge.

For a negative charge, the force points opposite your thumb.

When a charge moves parallel to the field ($\theta = 0^\circ$ or $180^\circ$), it feels no magnetic force. The maximum force happens when the charge moves perpendicular to the field ($\theta = 90^\circ$).

### Independent Forces from Electric and Magnetic Fields

In a region with both an electric field and a magnetic field, a moving charge feels two separate forces:

- The electric force: $F_E = qE$ (along the electric field for a positive charge)
- The magnetic force: $F_B = qvB\sin\theta$ (perpendicular to both velocity and field)

These forces act independently. Calculate each one separately, then add them as vectors to get the [net force](/ap-physics-2-revised/key-terms/net-force "fv-autolink") on the charge.

### Hall Effect

The Hall effect happens when charges moving through a conductor meet an external magnetic field that has a component perpendicular to their motion. The magnetic force pushes the moving charges sideways, so charge piles up on one side of the conductor and the opposite side ends up with the opposite charge. This separation creates a potential difference across the conductor, called the Hall [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink"). For AP Physics 2, describe this qualitatively as the result of the magnetic force acting on moving charges in the conductor.

> **Boundary Statement**
>
> On the exam, quantitative treatment of the magnetic force magnitude is limited to angles of 0°, 90°, and 180° between the velocity and magnetic field vectors. Qualitative analysis of other angles is permitted.

## How to Use This on the AP Physics 2 Exam

### Problem Solving

- Identify what you are given: charge, speed, field strength, and angle. Plug into $F_B = qvB\sin\theta$.
- For magnitude problems with an [electron](/ap-physics-2-revised/unit-15/2-the-bohr-model-of-atomic-structure/study-guide/gzEFr1ron8hpACPx "fv-autolink") or other negative charge, use the absolute value of the charge, then handle direction separately.
- Watch the angle. Quantitative force questions stick to $0^\circ$, $90^\circ$, and $180^\circ$, so $\sin\theta$ is usually 0 or 1.

### Free Response

- Do not stop at "right-hand rule." Walk through the steps: where your fingers point, how they curl, where your thumb ends up, and whether you flip it for a negative charge.
- When both fields are present, state clearly that the electric and magnetic forces are independent and show the vector addition.
- Tie any prediction about increasing or decreasing force back to the variable you changed in the equation.

### Common Trap

- The magnetic force never speeds up or slows down a charge, because it is always perpendicular to the velocity. It changes direction, not speed.

## Practice Problem 1: Magnetic Force on a Moving Charge

> An electron with charge -1.6 × 10^-19 C moves with a velocity of 2.0 × 10^6 m/s perpendicular to a uniform magnetic field of magnitude 0.50 T. Calculate the magnitude of the magnetic force experienced by the electron.

**Solution**

Use the magnetic force equation:

$$F_B = qvB\sin\theta$$

Since you want the magnitude, use the magnitude of the charge: $|q| = 1.6 × 10^{-19}$ C. Because the velocity is perpendicular to the field, $\sin 90^\circ = 1$.

$$F_B = |q|vB\sin\theta$$
$$F_B = (1.6 × 10^{-19} \text{ C})(2.0 × 10^6 \text{ m/s})(0.50 \text{ T})(1)$$
$$F_B = 1.6 × 10^{-13} \text{ N}$$

The magnitude of the force is 1.6 × 10^-13 N. To find the direction, use the right-hand rule for a positive charge and then reverse the result because the particle is an electron.

## Practice Problem 2: Magnetic Force with Parallel Motion

> A proton moves parallel to a uniform magnetic field of magnitude 0.40 T. What magnetic force does it experience?

**Solution**

Use the magnetic-force equation:

$$F_B = qvB\sin\theta$$

Because the proton moves parallel to the field, $\theta = 0^\circ$, so $\sin 0^\circ = 0$.

Therefore,

$$F_B = qvB(0) = 0$$

The magnetic force is $0\ \text{N}$.

## Common Misconceptions

- "A magnetic field always pushes on a charge." It only pushes on a charge that is moving and that has a velocity component perpendicular to the field. A still charge or a charge moving straight along the field feels no magnetic force.
- "The magnetic force does work on the charge." Because the force is always perpendicular to the velocity, it does no work and cannot change the charge's speed. It only bends the path.
- "The right-hand rule works the same for [electrons](/ap-physics-2-revised/key-terms/electrons "fv-autolink")." For negative charges, the force points opposite to what your right hand gives you, so always flip the result.
- "Electric and magnetic forces combine into one formula." In a region with both fields, treat the forces separately and add them as vectors.
- "Bigger angle always means bigger force." The force depends on $\sin\theta$, so it peaks at $90^\circ$ and drops to zero at $0^\circ$ and $180^\circ$, not steadily with angle.

## Related AP Physics 2 Guides

- [12.1 Magnetic Fields](/ap-physics-2-revised/unit-12/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ)
- [12.4 Electromagnetic Induction and Faraday's Law](/ap-physics-2-revised/unit-12/4-electromagnetic-induction-and-faradays-law/study-guide/UqgM4DyzPPfjroi3)
- [12.3 Magnetism and Current-Carrying Wires](/ap-physics-2-revised/unit-12/3-magnetism-and-current-carrying-wires/study-guide/TzaJHQDjTp5y8iuQ)

## Vocabulary

- **Hall effect**: The phenomenon in which a potential difference is created across a conductor when an external magnetic field perpendicular to the direction of charge motion is applied.
- **charge**: A fundamental property of matter that can be positive or negative, determining how objects interact electromagnetically.
- **charged object**: An object that possesses electric charge and can interact with electric and magnetic fields.
- **conductor**: A material through which electric charge can move, with resistivity that typically increases with temperature.
- **electric field**: A vector quantity that represents the electric force per unit charge exerted at a given point in space, originating from charged objects.
- **magnetic field**: A vector field that exerts a force on moving electric charges, electric currents, and magnetic materials.
- **magnetic force**: The force exerted by a magnetic field on a moving electric charge, electric current, or magnetic material.
- **perpendicular**: At a 90-degree angle; the magnetic field direction is perpendicular to both the velocity vector and the position vector from the charged object.
- **position vector**: A vector drawn from a moving charged object to a point in space, used to determine the magnetic field direction at that point.
- **right-hand rule**: A method for determining the direction of magnetic force, current, or magnetic field using the orientation of the right hand.
- **velocity**: The rate and direction of motion of a charged object, which affects the magnitude and direction of the magnetic field it produces.

## FAQs

### How do moving charges create magnetic fields?

A single moving charged object produces a magnetic field. The field depends on the charge’s velocity, the distance to the point being considered, and the angle between the velocity vector and the position vector.

### What is the magnetic force formula for a moving charge?

The magnetic force magnitude is F_B = qvB sin theta. It depends on charge, speed, magnetic field strength, and the angle between velocity and the magnetic field.

### When is magnetic force on a moving charge zero?

The magnetic force is zero when the charge is not moving or when its velocity is parallel or antiparallel to the magnetic field, so theta is 0 degrees or 180 degrees and sin theta is 0.

### When is magnetic force on a moving charge maximum?

The magnetic force is maximum when the velocity is perpendicular to the magnetic field. At theta = 90 degrees, sin theta = 1, so F_B = qvB for the magnitude.

### How do you use the right-hand rule for magnetic force?

For a positive charge, point your fingers in the direction of velocity, curl them toward the magnetic field, and your thumb points in the force direction. For a negative charge, reverse that direction.

### What is the AP Physics 2 boundary for magnetic-force angles?

Quantitative AP Physics 2 magnetic-force questions are limited to 0, 90, and 180 degrees between velocity and magnetic field. Other angles can be analyzed qualitatively.

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