Magnetic Force Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Magnetic Force.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The force exerted on a moving charge or current-carrying conductor by a magnetic field.

A moving charge in a magnetic field feels a sideways push — perpendicular to both its motion and the field. It's like a cross-wind deflecting a moving ball.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Magnetic force acts perpendicular to velocity — it changes direction but not speed.

Common stuck point: The force is zero when the charge moves parallel to the field — it's maximum when perpendicular.

Sense of Study hint: When solving a magnetic force problem, first identify whether it is a moving charge (F = qvB\sin\theta) or a current-carrying wire (F = BIL\sin\theta). Then find the angle \theta between the velocity (or current direction) and the magnetic field. Finally, use the right-hand rule to determine the direction of the force.

Worked Examples

Example 1

easy
A proton (q = 1.6 \times 10^{-19} \text{ C}) moves at 5 \times 10^6 \text{ m/s} perpendicular to a 0.3 \text{ T} magnetic field. What is the magnetic force on the proton?

Solution

  1. 1
    Use F = qvB\sin\theta with \theta = 90°.
  2. 2
    F = 1.6 \times 10^{-19} \times 5 \times 10^6 \times 0.3 \times 1
  3. 3
    F = 2.4 \times 10^{-13} \text{ N}

Answer

F = 2.4 \times 10^{-13} \text{ N}
The magnetic force on a moving charged particle is perpendicular to both the velocity and the magnetic field. It causes the particle to move in a circular path rather than speeding it up or slowing it down.

Example 2

medium
A wire carrying 8 \text{ A} is 0.5 \text{ m} long and placed at 60° to a 0.4 \text{ T} magnetic field. What force acts on the wire?

Example 3

medium
A proton (q = 1.6 \times 10^{-19} \text{ C}) moves at 3 \times 10^6 \text{ m/s} perpendicular to a 0.5 \text{ T} magnetic field. Find the magnetic force.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
An electron (q = 1.6 \times 10^{-19} \text{ C}, m = 9.11 \times 10^{-31} \text{ kg}) moves at 2 \times 10^7 \text{ m/s} perpendicular to a 0.01 \text{ T} field. What is the radius of its circular path?

Example 2

hard
Two parallel wires 0.1 \text{ m} apart each carry 10 \text{ A} in the same direction. What is the force per meter between them? Is it attractive or repulsive? Use \mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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