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JEE Main 202225 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
25 June
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2022 · 25 June · Morning Shift · Physics · Electromagnetic Waves

The electric field in an electromagnetic wave is given by E = 56 ....

The electric field in an electromagnetic wave is given by E=56.5sinω(t−xc)NC−1E = 56 . 5sin\omega\left(\dfrac{t - x}{c}\right){NC}^{- 1}. Find the intensity of the wave if it is propagating along xx-axis in the free space. (Given ϵ0=8.85×10−12C2N−1m−2{ϵ}_{0} = 8 . 85 \times {10}^{- 12}{C}^{2}{N}^{- 1}{m}^{- 2})

Options

  1. A5.65Wm−25 . 65{Wm}^{- 2}
  2. B1.9×10−7Wm−21 . 9 \times {10}^{- 7}{Wm}^{- 2}
  3. C4.24Wm−24 . 24{Wm}^{- 2}
  4. D56.5Wm−256 . 5{Wm}^{- 2}

Correct answer

C. 4.24Wm−24 . 24{Wm}^{- 2}

Step-by-step solution

Given, E=56.5sinω(t−xc)NC−1E = 56 . 5sin\omega\left(\dfrac{t - x}{c}\right)N{C}^{- 1}

Comparing it with the general equation of electromagnetic wave,

E=E0sin⁡(\omegat−kx)E = {E}_{0}\sin \left(\omegat - kx\right)

We have, E0=56.5NC−1{E}_{0} = 56 . 5N{C}^{- 1}

So, the intensity will be I=12ε0E02cI = \dfrac{1}{2}{ε}_{0}{E}_{0}^{2}c

=12×8.85×10−12×(56.5)2×3×108= \dfrac{1}{2} \times 8 . 85 \times {10}^{- 12} \times {\left(56 . 5\right)}^{2} \times 3 \times {10}^{8}

=4.24Wm−2= 4 . 24W{m}^{- 2}

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