Average energy density in an electromagnetic wave (22-24)

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Permeability of free space
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Review

The value of \(u\) at any position varies with time, so it’s often more useful to state its average value. The average value of the cosine function squared is \(1/2\), so

In Equation 22-24 we’ve used the root-mean-square (rms) values of the oscillating electric and magnetic fields, \(E_{\mathrm{average}} = E_0\ / \sqrt{2}\) and \(B_{\mathrm{rms}} = B_0\ / \sqrt{2}\) (see Section 21-2).