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An electromagnetic wave travelling through vacuum is described by $E = E_0\sin(\omega t - kx)$ and $B = B_0\sin(\omega t - kx)$. Which of the following equations is true?

1. $\omega B_0 = kE_0$
2. $kB_0 = \omega E_0$
3. $kE_0 = \omega B_0$
4. None of these

Correct answer: $\omega B_0 = kE_0$

Solution

In vacuum, a plane electromagnetic wave satisfies $E_0 = cB_0$. Also, for such a wave $c = \omega/k$. Combining these gives $E_0/B_0 = \omega/k$, or equivalently $\omega B_0 = kE_0$.

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