Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 2 / 18D / c / Solution

Transform the electromagnetic field tensor by $F^{\prime \mu \nu }={\Lambda }^{\mu }{}_{\alpha }{\Lambda }^{\nu }{}_{\beta }{F}^{\alpha \beta }$. For example,Reading off the other components in the same way yields the transverse field transformationThe longitudinal components remain $E_x^{\prime }=B_x^{\prime }=0$. These signs correspond to the stated boost in which $S^{\prime }$ moves with velocity $v$ relative to $S$.