Work done by a magnetic field on a moving charge

Magnetic fields do no work on charged particles that travel through them – at least, not by the definition of work in physics. So a charged particle in a magnetic field doesn’t gain or lose kinetic or potential energy. In this post, we will see how to find out the work done by a magnetic field on a moving charge.

Work done by a magnetic field on a moving charge is zero

The definition of work: W = Fs cos θ

In a magnetic field, the force on the charge and the direction of travel of the charge are always perpendicular to each other, which means, θ = 90°
And cos 90° = 0.
So the work done by a magnetic field on a moving charge, W = Fs cos θ, is automatically zero.

a charged particle in a magnetic field doesn’t gain or lose kinetic or potential energy

Therefore, the work done by a magnetic field on a moving charge is zero.
That’s why there’s no such thing as the magnetic potential to correspond to electric potential.
That’s all due to the physics definition of work – work changes the kinetic or potential energy of a system (or the energy is lost to heat), and nothing of the kind happens with magnetic fields. So a charged particle in a magnetic field doesn’t gain or lose kinetic or potential energy.

However, the direction of the charged particle does change, if the motion is not parallel to the external magnetic field.
Read more about the deflection of the charged particle in a magnetic field.