General Relativity: An Introduction for Physicists · Problem 6.11

Electromagnetism — Hobson, Efstathiou & Lasenby

Physics · charged-particle-3-acceleration

Problem

In some inertial frame

S

, show that the 3-acceleration of a charged particle in an electromagnetic field is

\vec{a} = \frac{d\vec{u}}{dt} = \frac{q}{\gamma m_0}\left[\vec{E} + \vec{u} \times \vec{B} - \frac{1}{c^2}(\vec{u}\cdot\vec{E})\vec{u}\right].