Consider the example of a positive charge q moving in the negative z-direction with speed v with the local magnetic field of magnitude B in the z-direction.

Find F, the magnitude of the magnetic force acting on the particle. Express your answer in terms of v, q, B, and other quantities given in the problem statement.

F = 0

Explanation:

This problem can be solved by using the equation for the force produced by a magnetic field over a charge

F = qv X B

That is, the cross product between velocity and the magnetic field.

In this case, v is in the negative z-direction v = - v k^,

and the magnetic field is in the positive z-direction B = z k^

Hence, the cross product is

F = qv X B = 0i^ - 0j^ + 0k^ = 0

In this case the net force is zero due to both velocity and magnetic field vectors are in the z-direction