Which of the following is true about electric field \( (\vec{E}) \) and magnetic field \( (\vec{B}) \) of electromagnetic waves?
A. \( \vec{E} \) and \( \vec{B} \) are perpendicular to each other.
B. \( \vec{E} \) and \( \vec{B} \) differ in phase by \( \pi \).
C. The energy density associated with \( \vec{E} \) and energy density associated with \( \vec{B} \) are same.
D. \( \vec{E} \) and \( \vec{B} \) are parallel
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A and C only
In an electromagnetic wave, \( \vec{E} \) and \( \vec{B} \) oscillate in phase, at right angles to each other and to the direction of propagation, with \( E_{0} = cB_{0} \).
(A) \( \vec{E} \) and \( \vec{B} \) are perpendicular to each other. — Correct. The wave is transverse: \( \vec{E} \), \( \vec{B} \) and the direction of propagation are mutually perpendicular, and \( \vec{E}\times\vec{B} \) points along the direction of travel.
(B) \( \vec{E} \) and \( \vec{B} \) differ in phase by \( \pi \). — Incorrect. They are in phase: both reach their maximum and their zero at the same place and time.
(C) The energy density associated with \( \vec{E} \) and energy density associated with \( \vec{B} \) are same. — Correct. Using \( B = E/c \) and \( c^{2} = 1/(\mu_{0}\varepsilon_{0}) \), the two energy densities are equal.
\( \displaystyle u_{B} = \frac{B^{2}}{2\mu_{0}} = \frac{E^{2}}{2\mu_{0}c^{2}} = \frac{1}{2}\varepsilon_{0}E^{2} = u_{E} \)
(D) \( \vec{E} \) and \( \vec{B} \) are parallel — Incorrect. They are perpendicular, as explained in (A).
NCERT (2026-27):
Summary – “… The oscillating electric and magnetic fields, E and B are perpendicular to each other, and to the direction of propagation of the electromagnetic wave.”
Exercises – “… (c) Show that the average energy density of the E field equals the average energy density of the B field.”