The electric field in an electromagnetic wave is given by $\mathrm{E}=56.5 \sin \omega(\mathrm{t}-\mathrm{x} / \mathrm{c}) \mathrm{NC}^{-1}$. Find the intensity of the wave if it is propagating along $x$-axis in the free space. (Given $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

(C) $1.9 \times 10^{-7} \mathrm{Wm}^{-2}$

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · EM Waves

The electric field in an electromagnetic wave is given by

E = 56.5 sin ω (t - x / c) NC^{- 1}

. Find the intensity of the wave if it is propagating along

x

-axis in the free space. (Given

ε_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}

)

Answer: (B)

The intensity of an electromagnetic wave is given by:

I = \frac{1}{2} ε_{0} E_{0}^{2} c

where

E_{0} = 56.5

N/C is the amplitude of the electric field,

ε_{0} = 8.85 \times 1 0^{- 12}

C²N⁻¹m⁻², and

c = 3 \times 1 0^{8}

m/s.

Substituting:

I = \frac{1}{2} \times (8.85 \times 1 0^{- 12}) \times (56.5)^{2} \times (3 \times 1 0^{8})

I = \frac{1}{2} \times 8.85 \times 1 0^{- 12} \times 3192.25 \times 3 \times 1 0^{8}

I \approx 4.24 Wm^{- 2}

Answer: (B)

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option