Question

There is a straight wire with current whose direction points upward. There is some particle with +q charge at rest some distance away from the wire.

What would be the direction of the force acting on the particle? and magnitude? what kind of motion would the particle undergo?

Answer 1

I am assuming here that current in the wire is constant here.

Magnetic force is given as F = q(v X B)

since particle here is at rest so v = 0

Hence there won't be any force acting on it. F = 0

More precise part:

BUT if the charge in question has magnetic 'spin' or dipole moments and since magnetic field produced by current carrying wire is non-uniform (1/r dependence), charge will travel along with it.