Introduction to Electrodynamics · Problem 12.41

Electrodynamics and Relativity — David J. Griffiths

Physics · relativistic-dynamics-electromagnetic

Problem

Show that the (ordinary) acceleration of a particle of mass

m

and charge

q

, moving at velocity

\mathbf{u}

under the influence of electromagnetic fields

\mathbf{E}

and

\mathbf{B}

, is given by

\mathbf{a} = \frac{q}{m}\sqrt{1-u^2/c^2}\left[\mathbf{E} + \mathbf{u}\times\mathbf{B} - \frac{1}{c^2}\mathbf{u}(\mathbf{u}\cdot\mathbf{E})\right].

[Hint: Use Eq. 12.74.]