Concept:

Electric forces can do work on a charge, speeding it up or slowing it down. Magnetic forces, however, always act perpendicular to the velocity vector of the charge.

Formula:

$$ W = \mathbf{F}_m \cdot \mathbf{v} dt = q(\mathbf{v} \times \mathbf{B}) \cdot \mathbf{v} dt = 0 $$

Solution:

• Because the magnetic force is always perpendicular to velocity, the dot product of force and velocity is zero.



• This means magnetic forces do absolutely no mechanical work (\( W = 0 \)) on a moving charge.



• By the work-energy theorem, if no work is done, kinetic energy (and thus speed or velocity magnitude) remains constant.



• The perpendicular force acts strictly as a centripetal force, altering only the direction of the velocity vector.

Why other options are incorrect:

Option A is false because magnetic fields cannot change speed. Option C conflates magnetic forces with electric forces. Option D is false because a force must cause an acceleration, which is a change in velocity (direction in this case).