[UPSC IFoS 2022] Electromagnetic Theory (Q316, 15M)

A relativistic charged particle moves in the space occupied by uniform and mutually perpendicular electric and magnetic fields \vec{\text{E}} = \text{E}_0\,\hat{\text{x}} and \vec{\text{B}} = \text{B}_0\,\hat{\text{y}}, respectively. The particle moves rectilinearly along the z-direction. Find \vec{\text{E}}' and \vec{\text{B}}' in the reference frame moving translationally with the particle.