Question

A point charge \( q \) is moving with velocity \( \mathbf{v} \) in a uniform magnetic field \( \mathbf{B} \). Find the work done by the magnetic force on the charge.

Hint:

The magnetic force on a charged particle does no work since it acts perpendicular to the velocity of the particle, causing no change in its kinetic energy.

Answer 1

The work done by a force is given by: \[ W = \mathbf{F} \cdot \mathbf{d} \] Where \( \mathbf{F} \) is the force and \( \mathbf{d} \) is the displacement. The magnetic force on a moving charge is given by: \[ \mathbf{F} = q \mathbf{v} \times \mathbf{B} \] Since the magnetic force is always perpendicular to the velocity of the particle, the work done by the magnetic force is zero because: \[ W = \mathbf{F} \cdot \mathbf{d} = 0 \] Therefore, the magnetic force does no work on a moving charge, as it does not change the kinetic energy of the particle.