Electromagnetic duality

Vacuum Maxwell equations without sources are invariant under $E^{\prime }=E\cos \alpha +cB\sin \alpha$, $c{B}^{\prime }=cB\cos \alpha -E\sin \alpha$. At $\alpha =\pi /2$ this is $E^{\prime }=cB$, $B^{\prime }=-E/c$. Electric-conductor boundary conditions are not invariant under arbitrary duality rotations; the transformed fields must be tested separately against the wall conditions.