Daniel B. answered 05/30/21
A retired computer professional to teach math, physics
a. The magnetic force is perpendicular to the particle velocity, because
the force is the VECTOR PRODUCT of the velocity and the magnetic field.
And any force perpendicular to velocity does no work, because work is the
DOT PRODUCT of force and distance.
b. The magnetic field is indeed conservative, but that property implies zero work
only for a particle that completes a circle.
c. It is true that work is a scalar and the other quantities are vectors,
but that does not imply zero work.
d. The magnetic force is indeed a velocity-dependent force, but that does not
imply zero work.
e. The force is indeed acting on a moving particle, but work is proportional to
the cosine of the angle between the force and velocity, which in this case is 0.