Show that the Cartesian components of the transverse current density j⊥(r, t) used to define the Coulomb gauge vector potential can be written in terms of the total current density j(r, t) as

where the transverse delta function is

Transcribed Image Text:

j_.x(x, t) = [ d³r¹ $ž (r— r')je(r', t), jL,k(r, -