The energy density associated with electric field $\vec{E}$ and magnetic field $\overrightarrow{\mathrm{B}}$ of an electromagnetic wave in free space is given by ($\epsilon_{0}$ - permittivity of free space, $\mu_{0}$ - permeability of free space)

(D) $\mathrm{U}_{\mathrm{E}}=\frac{\in_{0} \mathrm{E}^{2}}{2}, \mathrm{U}_{\mathrm{B}}=\frac{\mathrm{B}^{2}}{2 \mu_{0}}$

(A) $\mathrm{U}_{\mathrm{E}}=\frac{\mathrm{E}^{2}}{2 \epsilon_{0}}, \mathrm{U}_{\mathrm{B}}=\frac{\mathrm{B}^{2}}{2 \mu_{0}}$

(B) $U_{E}=\frac{E^{2}}{2 \epsilon_{0}}, U_{B}=\frac{\mu_{0} B^{2}}{2}$

(C) $\mathrm{U}_{\mathrm{E}}=\frac{\in_{0} \mathrm{E}^{2}}{2}, \mathrm{U}_{\mathrm{B}}=\frac{\mu_{0} \mathrm{~B}^{2}}{2}$

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · EM Waves

The energy density associated with electric field

E

and magnetic field

B

of an electromagnetic wave in free space is given by (

ϵ_{0}

- permittivity of free space,

μ_{0}

- permeability of free space)

(A) $U_{E} = \frac{E ^{2}}{2 ϵ _{0}}, U_{B} = \frac{B ^{2}}{2 μ _{0}}$
(B) $U_{E} = \frac{E ^{2}}{2 ϵ _{0}}, U_{B} = \frac{μ _{0} B ^{2}}{2}$
(C) $U_{E} = \frac{\in _{0} E ^{2}}{2}, U_{B} = \frac{μ _{0} B ^{2}}{2}$
(D) $U_{E} = \frac{\in _{0} E ^{2}}{2}, U_{B} = \frac{B ^{2}}{2 μ _{0}}$ ✓ Correct

Answer: (D)

The energy stored per unit volume in an electric field is

U_{E} = \frac{1}{2} ϵ_{0} E^{2}

, and the energy stored per unit volume in a magnetic field is

U_{B} = \frac{B ^{2}}{2 μ _{0}}

. These are the energy densities of the electric and magnetic fields of the wave in free space.

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option