Consider a point particle with charge q.
(a) Start with the field vec(E) of a point charge at rest - i.e., the Coulomb field. Then, calculate
the electric field vec(E)^(') for a frame in which the particle moves with constant velocity vec(v)=vhat(x).
Use the rules for how vec(E) fields transform under Lorentz boosts.
(b) Use the results for retarded fields and calculate vec(E) for a particle moving with constant
velocity vec(v)=vhat(x).
Is this answer different from part (a)? If so, why? Can you comment on the magnetic
fields in both situations?
(a) Start with the field E of a point charge at rest -- i.e., the Coulomb field. Then, calculate the electric field E' for a frame in which the particle moves with constant velocity 1 = vx Use the rules for how E fields transform under Lorentz boosts.
(b) Use the results for retarded fields and calculate E for a particle moving with constant velocity = vi. Is this answer different from part (a)? If so, why? Can you comment on the magnetic fields in both situations?