Which of the following statements about a plane electromagnetic wave…

The correct answer is Option (2) → The average energy density of the electric field is \( c \) times the average energy density of the magnetic field.

An electric field stores energy \( \frac{1}{2}\varepsilon_0E^{2} \) per unit volume. A magnetic field stores \( B^{2}/2\mu_0 \). In a plane wave in vacuum, \( B=E/c \) at every point and instant. Also, \( c^{2}=1/\mu_0\varepsilon_0 \). Putting these in the magnetic energy density gives:

    \( \begin{aligned} u_B &= \frac{B^{2}}{2\mu_0} \\ &= \frac{E^{2}}{2\mu_0c^{2}} \\ &= \frac{1}{2}\varepsilon_0E^{2} \end{aligned} \)

So \( u_B=u_E \) at every point and at every instant. The energy of the wave is shared equally between its electric and magnetic fields.

Option (1) The energy density of the electric field at a point is \( \frac{1}{2}\varepsilon_0E^{2} \), where \( E \) is the electric field at that point. — Correct statement. This expression holds for an electric field in any region of space, including the field of the wave.

Option (2) The average energy density of the electric field is \( c \) times the average energy density of the magnetic field. — Not correct. The factor \( c \) links the magnitudes of the fields, \( E=cB \). The energy densities depend on \( \varepsilon_0E^{2} \) and \( B^{2}/\mu_0 \). These come out equal, so their averages are equal too.

Option (3) The energy density of the magnetic field at a point is \( B^{2}/2\mu_0 \), where \( B \) is the magnetic field at that point. — Correct statement. This is the magnetic energy per unit volume, valid wherever a magnetic field exists.

Option (4) The amplitudes of the electric and magnetic fields are related by \( E_0=cB_0 \). — Correct statement. In vacuum the amplitudes satisfy \( B_0=E_0/c \), which is the same relation.

NCERT (2026-27):
Example 6.9 – “(b) The magnetic energy per unit volume is,”

    \( \displaystyle u_B=\frac{U_B}{V}= \)\( \displaystyle \frac{B^{2}}{2\mu_0} \)\( \qquad (6.18) \)

“We have already obtained the relation for the electrostatic energy stored per unit volume in a parallel plate capacitor (refer to Chapter 2, Eq. 2.73),”

    \( \displaystyle u_E=\frac{1}{2}\varepsilon_0E^{2} \)\( \qquad (2.73) \)

“In both the cases energy is proportional to the square of the field strength. Equations (6.18) and (2.73) have been derived for special cases: a solenoid and a parallel plate capacitor, respectively. But they are general and valid for any region of space in which a magnetic field or/and an electric field exist.”