Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle?

Question

Which one of the following statements best

explains why a constant magnetic field can do no work on a moving charged particle?

A) The magnetic field is conservative.

B) The magnetic force is a velocity dependent force.

C) The magnetic field is a vector and work is a scalar quantity.

D) The magnetic force is always perpendicular to the velocity of the particle.

E) The electric field associated with the particle cancels the effect of the magnetic field on the particle.

The answer is D but please explain why. Why can't it be B?

Answer 1

Although the magnetic force is a "velocity dependent force" as in: F_B = q(v×B) (× here is the cross-product), the cross-product "forces" (a good place for a pun here) the magnetic force, F_B to always be perpendicular to both the velocity, v, and the magnetic field, B.

Since work is defined as W = F•D, where • is the dot-product and D is given by the product of the particle velocity and the time, vt, you can see that W must be equal to zero. This is because W = F_B·vt·cos(θ), where θ--the angle between the initial magnetic force, F_B, and the velocity, v--is equal to 90° due to the cross product between v and B in the original definition of F_{B =} q(v×B).

In other words, the magnetic force causes charged particles to circle around the magnetic field lines, always perpendicular to the particle's linear velocity.