Question

A standing electromagnetic wave `E=E_(m) cos kx. Cosomegat` is sustained along the `x` axis in vacuum. Find the projection of the Poyntind vector on the `x` axis `S_(x)(x,t)` and the mean value of that projection averaged over an oscillation period.

Answer 1

`oversetrarr(E) = oversetrarr(E_(m)) cos kx omega t`
`oversetrarr(H) = (oversetrarr(k) xx oversetrarr(E_(m)))/(mu_(0)omega) sin kx sin omegat`
`oversetrarr(S) = oversetrarr(E) xx oversetrarr(H) = (oversetrarr(E_(m)) xx (oversetrarr(k)xx oversetrarr(E)_(m)))/(mu_(0)omega) (1)/(4) sin 2kx sin 2 omegat`
Thus `S_(x) = (1)/(4) epsilon_(0) cE_(m)^(2) sin 2kx sin 2 omegat` (as `(1)/(mu_(0)c) = epsilon_(0)c)`