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An electromagnetic wave travels along the z-axis. Which of the following pairs of space- and time-varying fields would generate such a wave?

1. \(\vec E\) along y, \(\vec B\) along x
2. \(\vec E\) along x, \(\vec B\) along y
3. \(\vec E\) along x, \(\vec B\) along z
4. \(\vec E\) along z, \(\vec B\) along y

Correct answer: \(\vec E\) along x, \(\vec B\) along y

Solution

For a wave traveling along the z-axis, both \(\vec E\) and \(\vec B\) must be perpendicular to z and to each other. The pair \(\vec E\) along x and \(\vec B\) along y gives \(\vec E \times \vec B\) along z.

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