General Relativity: An Introduction for Physicists · Problem 6.7

Electromagnetism — Hobson, Efstathiou & Lasenby

Physics · lorentz-transformation-fields-arbitrary-boost

Problem

Show that one may eliminate the explicit reference to the projections of

\vec{E}

and

\vec{B}

in Exercise 6.6 and write the transformations as

\vec{E}' = \gamma(\vec{E} + \vec{v} \times \vec{B}) + \frac{1-\gamma}{v^2}(\vec{v}\cdot\vec{E})\vec{v},

\vec{B}' = \gamma\left(\vec{B} - \frac{1}{c^2}\vec{v} \times \vec{E}\right) + \frac{1-\gamma}{v^2}(\vec{v}\cdot\vec{B})\vec{v}.