(a) Boost from the laboratory frame K to the rest frame K' to find the vector potential A(r, t) and the scalar potential ϕ(r, t) for a charged particle q which moves with constant velocity v when viewed from the laboratory.
(b) Find E and B in the laboratory frame using the potentials computed in part (a).
(c) Let r = r_⊥ + r_ΙΙ be the decomposition of the position vector into components perpendicular and parallel to v. In the limit when ν → c, show that the fields you computed in part (b) reduce to

Interpret your result in terms of the Lorentz contraction.
(d) Compare and contrast the fields in part (c) with the radiation fields produced by a compact time dependent source.

Transcribed Image Text:

E(r, t) = = 1 r₁ Σπερ ri -q8(ct-r) and B(r, t) = Ho V x r₁ 2rr² -q8(ct - r).