(a) Show that Maxwell's equations with magnetic charge (Eq.7.43) are invariant under the duality transformation where c ?? 1/ ??ε0?0 and a is an arbitrary rotation angle in "E/B-space." Charge and current densities transform in the same way as qe and qm. [This means, in particular, that if you know the fields produced by a configuration of electric charge, you can immediately (using a = 90o) write down the fields produced by the corresponding arrangement of magnetic charge.]

(b) Show that the force law (Prob. 7.35) is also invariant under the duality transformation.

Transcribed Image Text:

E' cB' cq'e 9m E cos acB sina, cB cos a Esin a. cge cosa + qm sina, 9m cosa cqe sina, F=qe (E+vx B) + qm (B VX E)