A surface current density K(r_S, t) flows in the z = 0 plane which separates region 1 (z > 0) from region 2 (z < 0). Each region contains arbitrary, time-dependent distributions of charge and current.

(a) For fields B(r, t) and E(r, t), use the theta function method of the text to derive a matching condition based on the Ampere-Maxwell law:

(b) Explain how to adapt this result to an interface which is not flat.

Transcribed Image Text:

V x B = мој + 1 ӘE 22 at