The following have zero average value in a plane electromagnetic wave

The correct answer is Option (3) → both electric field and magnetic field

In a plane electromagnetic wave both fields vary sinusoidally and in phase.

    \( \displaystyle E = E_0\sin(kx - \omega t), \qquad B = B_0\sin(kx - \omega t) \)

A sine function is positive for half a cycle and negative for the other half, so the time average of each field is zero. The energy densities \( \varepsilon_0E^{2}/2 \) and \( B^{2}/2\mu_0 \) contain the squares of the fields, which are never negative, so their averages are not zero.

Option (1) electric field only — Incorrect. The magnetic field also averages to zero, so "only" is wrong.

Option (2) magnetic field only — Incorrect. The electric field also averages to zero.

Option (3) both electric field and magnetic field — Correct. Both fields are sinusoidal and average to zero over a cycle.

Option (4) both electric energy and magnetic energy — Incorrect. The energy densities depend on \( E^{2} \) and \( B^{2} \), which are never negative, so their averages are not zero.