Introduction to Electrodynamics · Problem 10.4

Potentials and Fields — David J. Griffiths

Physics · vector-potential-plane-wave

Problem

Suppose

V = 0

and

\mathbf{A} = A_0\sin(kx - \omega t)\hat{\mathbf{y}}

, where

A_0

\omega

, and

k

are constants. Find

\mathbf{E}

and

\mathbf{B}

, and check that they satisfy Maxwell's equations in vacuum. What condition must you impose on

\omega

and

k