A charge density (r, t) = q(t )(r) where q(t ) = 0 for t . (a)

A charge density ρ(r, t) = q(t )δ(r) where q(t ) = 0 for t τ.
(a) Calculate E(r, t) and B(r, t) using symmetry and elementary methods.
(b) Calculate E(r, t) and B(r, t) from the Coulomb gauge scalar and vector potentials.
(c) Calculate E(r, t) and B(r, t) from the Lorenz gauge scalar and vector potentials. As an intermediate step, you will prove that

Use an extra integration over t and a delta function δ(t' − t + |r − r'|/c) to impose retardation of the vector potential in part (c).

Transcribed Image Text:

[d's 8(T-s/c) |rs| [²00 r = 4π -O(rct)O(T) + c²TO(ct-r) x-1)].