(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 qe and qm.
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.
Assuming that “Coulomb’s law” for magnetic charges (qm) reads
work out the force law for a monopole qm moving with velocity v through electric and magnetic fields E and B.26
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