Question

Consider the following two statements regarding a linearly polarised, plane electromagnetic wave:
(A) The electric field and the magnetic field have equal average values.
(B) The electric energy and the magnetic energy have equal average values.
(a) Both A and B are true.
(b) A is false but B is true.
(c) B is false but A is true
(d) Both A and B are false.

Answer 1

(a) Both A and B are true.
For a linearly polarised, plane electromagnetic wave
$$\begin{gathered} E=E_0\sin \omega (t-\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$c$}\right.) \\ B=B_0\sin \omega (t-\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$c$}\right.) \end{gathered}$$
The average value of either E or B over a cycle is zero ( average of sin($\theta$) over a cycle is zero).
Also the electric energy density (u_E) and magnetic energy density (u_B)are equal.
$u_{\mathrm{E}}=\frac{1}{2}{\in }_0{E}^2=\frac{B^2}{2{\mu }_0}=u_{\mathrm{B}}$
Energy can be found out by integrating energy density over the entire volume of full space.
As the energy of the electromagnetic wave is equally shared between electric and magnetic field so their average values will also be equal.