Identify the correct statements among the following.
A. Electric and magnetic fields have zero average value in a plane EM wave.
B. For an EM wave in free space, the ratio of \( \omega/k \) is independent of wavelength.
C. In an EM wave, the \( E \) and \( B \) fields vary with same frequency and are in opposite phase.
D. The energy associated with electric field is much greater than that associated with the magnetic field.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A and B only
In a plane electromagnetic wave E and B oscillate sinusoidally at the same frequency, in phase, with \( E_0 = cB_0 \), and travel at c in free space.
(A) Electric and magnetic fields have zero average value in a plane EM wave. — Correct. Each field varies as a sine function, for example \( E = E_0\sin(kx - \omega t) \), which is positive and negative for equal times, so its average over a cycle is zero.
(B) For an EM wave in free space, the ratio of \( \omega/k \) is independent of wavelength. — Correct. \( \omega/k \) is the wave speed, and in free space every electromagnetic wave travels at c whatever its wavelength.
\( \omega/k = c = 3\times10^{8}\,\mathrm{m/s} \)
(C) In an EM wave, the \( E \) and \( B \) fields vary with same frequency and are in opposite phase. — Incorrect. They do have the same frequency, but they are in the same phase: both reach their maximum and zero values at the same place and time.
(D) The energy associated with electric field is much greater than that associated with the magnetic field. — Incorrect. The two energy densities are equal, using \( E = cB \) and \( c^{2} = 1/(\mu_0\varepsilon_0) \).
\( \displaystyle u_E = \frac{1}{2}\varepsilon_0E^{2} = \frac{1}{2}\varepsilon_0c^{2}B^{2} = \frac{B^{2}}{2\mu_0} = u_B \)