 Solution

Use ideal large plates and neglect edge effects. A Lorentz boost normal to the plates does not contract either transverse plate dimension. Charge is invariant, so charge per plate area remains ${\sigma }^{\prime }=\sigma$. Gauss's law then givesThe plate separation contracts, but the infinite-plate field is independent of separation. It is therefore incorrect to infer a stronger field merely from the shorter gap. The ideal field is parallel to the boost, so there is no induced transverse magnetic field from this boost.