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

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Question

Magnetic field magnitude

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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).