Question

A point charge q is moving with velocity `vec v` in a uniform magnetic field `vec B`. Find the work done by the magnetic force on the charge.

Answer 1

The magnetic force is always perpendicular to the velocity v because of the cross product.

Since displacement dr is in the direction of v, we have:

dW = q(v × B). v

Using the vector identity (A × B).C = 0 if C = A we get:

dW = 0

So, the work done per infinitesimal displacement is always zero; the overall work done by the magnetic force on the charge is also zero, regardless of how the charge moves. The magnetic field simply changes the direction of motion of the charge, not its speed or kinetic energy.