Introduction to Electrodynamics · Problem 10.20

Potentials and Fields — David J. Griffiths

Physics · lienard-wiechert-fields

Problem

Suppose a point charge

q

is constrained to move along the

x

axis. Show that the fields at points on the axis to the right of the charge are given by

\mathbf{E} = \frac{q}{4\pi\epsilon_0} \frac{1}{\mathit{z}^2}\left(\frac{c+v}{c-v}\right)\hat{\mathbf{x}}, \quad \mathbf{B} = \mathbf{0}.

(Do not assume

v

is constant!) What are the fields on the axis to the left of the charge?