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In an electromagnetic wave in free space, the root mean square value of the electric field is $E_{\text{rms}} = 6\,\text{V/m}$. The peak value of the magnetic field is:

1. 1.41 × 10^-8 T
2. 2.83 × 10^-8 T
3. 0.70 × 10^-8 T
4. 4.23 × 10^-8 T

Correct answer: 2.83 × 10^-8 T

Solution

For an electromagnetic wave in free space, $E_0 = cB_0$ and $E_{\text{rms}} = E_0/\sqrt{2}$. So $E_0 = 6\sqrt{2}$ V/m, and $B_0 = E_0/c = 6\sqrt{2}/(3\times10^8)$. This gives $B_0 \approx 2.83\times10^{-8}$ T.

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