Force on a moving charge in a magnetic field

A magnetic field exerts a force on a moving charge.

The force on a moving particle is calculated as a cross product of the particle's velocity and the magnetic field's strength.

In a magnetic field, B, a charge, q, moving with velocity, v, experiences a force, F:

F = q (v x B)

Magnetic field strength is measured in tesla (T), where 1 T = 1 kg s-2A-1

We can express this without using the cross product (which is not needed at A level).

F = Bqv sinθ

You can determine the direction of the force vector by using the left-hand rule

You can calculate the magnitude of the magnetic force vector, as long as you know the angle θ between the velocity vector and the magnetic field vector.

Example Question

A charge of +5.0 C moves upward at 2.0 ms-1 in a magnetic field of 0.30 T that points into the plane of the page as shown in the diagram.

What is the magnitude and direction of the force that the charge experiences?

The field is at right angles to the velocity so sin θ = 1

Therefore the magnitude of F = 0.30 x 5.0 x 2.0 = 3.0 N

Using FLHR the charge experiences a force to the left.


See this page for experimental details