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JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2019 · 12 April · Evening Shift · Physics · Electromagnetic Waves

A plane electromagnetic wave having a frequency f = 23.9GHz...

A plane electromagnetic wave having a frequency f=23.9GHzf = 23.9GHz propagates along the positive z−z - direction in free space. The peak value of the Electric Field is 60V/m.60V / m . Which among the following is the acceptable magnetic field component in the electromagnetic wave?

Options

  1. A\overset{\to}{B} = 2 \times {10}^{- 7}sin \left(0.5 \times {10}^{3}z - 1.5 \times {10}^{11}t\right)\overset{^}{i}
  2. B\overset{\to}{B} = 2 \times {10}^{- 7}sin \left(1.5 \times {10}^{3}x + 0.5 \times {10}^{11}t\right)\overset{^}{j}
  3. C\overset{\to}{B} = 2 \times {10}^{7}sin \left(0.5 \times {10}^{3}z + 1.5 \times {10}^{11}t\right)\overset{^}{i}
  4. D\overset{\to}{B} = 60sin \left(0.5 \times {10}^{3}x + 1.5 \times {10}^{11}t\right)\overset{^}{i}

Correct answer

A. \overset{\to}{B} = 2 \times {10}^{- 7}sin \left(0.5 \times {10}^{3}z - 1.5 \times {10}^{11}t\right)\overset{^}{i}

Step-by-step solution

B=Ec=603×108=2×10−7B = \dfrac{E}{c} = \dfrac{60}{3 \times {10}^{8}} = 2 \times {10}^{- 7}
The magnetic field can be written as,
k=2πλ=2πc/f≈500k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{c / f} \approx 500
ω=2\pif≈1.5×1011\omega = 2\pif \approx 1.5 \times {10}^{11}
\overset{\to}{B} = 2 \times {10}^{- 7}\sin (0.5 \times {10}^{3}z - 1.5 \times {10}^{11}t ) \overset{^}{i}
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