Past exam of the symmetry and relativity course of the University of Oxford / 2017 / 4 / a

For a boost along positive $x$, let $\gamma =(1-v_x^2/c^2{)}^{-1/2}$. Parallel field components are unchanged, while transverse components mix. The Lorentz transformation of electromagnetic fields givesThese signs correspond to $S^{\prime }$ moving with $+v_x$ relative to $S$, not the inverse boost. They can be obtained from $F^{\prime }=\Lambda F{\Lambda }^{\mathsf{T}}$ for the electromagnetic field tensor.