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 field 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

Answer: (A)

Both (A) and (B) are true.

E and B are sinusoidal functions and have average value zero over a cycle respectively.
$E=E_0\sin (kz-\omega t)$
$B=B_0\sin (kz-\omega t+\frac{\pi }{2})$
E and B are sinusoidal functions and have average value zero over a cycle respectively.
Energy density for electric field: $\frac{1}{2}{ϵ}_0{E}^2$
Energy density for magnetic field: $\frac{1}{2{\mu }_0}{B}^2$
Since $E=cB$ where $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
both energy densities are equal.