A particle of charge q1 is at rest at the origin. A second particle, of charge q2, moves...

A particle of charge q₁ is at rest at the origin. A second particle, of charge q₂, moves along the z axis at constant velocity v.

(a) Find the force F₁₂(t) of q₁ on q₂, at time t (when q2 is at z = vt).

(b) Find the force F₂₁(t) of q₂ on q₁, at time t. Does Newton’s third law hold, in this case?

(c) Calculate the linear momentum p(t) in the electromagnetic fields, at time t. (Don’t bother with any terms that are constant in time, since you won’t need them in part (d)).

(d) Show that the sum of the forces is equal to minus the rate of change of the momentum in the fields, and interpret this result physically.