Pointing to the Poynting!

Electricity and Magnetism Level 4

Find the mean Poynting vector of a plane electromagnetic wave \(\textbf{E} = {\textbf{E}}_{m}cos(\omega t - \textbf{k}\textbf{r})\) if the wave propagates in vacuum.

If the answer can be written as

\[\displaystyle {S}_{av} = \frac{a}{b} {{\mu}_{0}}^{c}{{\textbf{E}}_{m}}^{d}{\textbf{k}}^{e}{\omega}^{f}\]

where \(a,b,c,d,e\) are positive reals.

Give your answer as \(\displaystyle a + b + c + d + e + f\)


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