Question

What is the work done by an external uniform magnetic field perpendicular to the velocity of a moving charge?

Answer 1

1. The work done by an external uniform magnetic field on a moving charge is zero when the field is perpendicular to the velocity of the charge. This is because the magnetic force always acts perpendicular to the direction of motion of the charge.
2. Since work is given by the dot product of force and displacement, and the magnetic force is always perpendicular to displacement, the work done is zero. The magnetic field does not change the speed or kinetic energy of the charge; it only alters its direction.
3. As a result, the charged particle undergoes circular or helical motion, depending on its velocity components. However, since there is no change in kinetic energy, the magnetic field does no work on the charge.