JEE Main · 2023 · 11 Apr 2023 · Shift 1 · EM Waves

The electric field in an electromagnetic wave is given as

E = 20 sin ω (t - \frac{x}{c}) j NC^{- 1}

, where

ω

and

c

are the angular frequency and the velocity of the electromagnetic wave. The total energy contained in a volume of cross-sectional area

10 cm^{2}

and length

50 cm

(volume

5 \times 1 0^{- 4} m^{3}

) taken along the direction of propagation is ______ J.
(Given

ε_{0} = 8.85 \times 1 0^{- 12} C^{2} / Nm^{2}

)

Answer: (C)

Solution

The energy carried by the wave is the product of its average energy density and the volume considered. For the field amplitude

E_{0} = 20

N/C the average total energy density is

u = \frac{1}{2} ε_{0} E_{0}^{2}

. Taking the region as the cylinder of cross-section

10 cm^{2}

and length

50 cm

, the volume is

V = 5 \times 1 0^{- 4}

^{3}

. Hence the energy is

u V = \frac{1}{2} (8.85 \times 1 0^{- 12}) (20)^{2} (5 \times 1 0^{- 4}) = 8.85 \times 1 0^{- 13}

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option