Use the “duality” transformation of Prob. 7.64, together with the fields of an oscillati...

Use the “duality” transformation of Prob. 7.64, together with the fields of an oscillating electric dipole (Eqs. 11.18 and 11.19), to determine the fields that would be produced by an oscillating “Gilbert” magnetic dipole (composed of equal and opposite magnetic charges, instead of an electric current loop). Compare Eqs. 11.36 and 11.37, and comment on the result.

Reference equation 11.36 and 11.37

Reference prob 7.64.

(a) Show that Maxwell’s equations with magnetic charge (Eq. 7.44) are invariant under the duality transformation

where is an arbitrary rotation angle in “E/B-space.” Charge and current densities transform in the same way as q_e and q_m.

particular, that if you know the fields produced by a configuration of electric charge, you can immediately (using α = 90^?) write down the fields produced by the corresponding arrangement of magnetic charge.]

(b) Show that the force law (Prob. 7.38)

is also invariant under the duality transformation.