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

(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.

Problem 7.38

Assuming that “Coulomb’s law” for magnetic charges (q_m) reads

work out the force law for a monopole qm moving with velocity v through electric and magnetic fields E and B.²⁶