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JEE Main 202226 JulyMorning Shift
Exam
JEE Main
Year
2022
Date
26 July
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2022 · 26 July · Morning Shift · Physics · Electromagnetic Waves

The magnetic field of a plane electromagnetic wave is given by → B...

The magnetic field of a plane electromagnetic wave is given by \overset{\to}{B} = 2 \times {10}^{- 8}\sin \left(0 . 5 \times {10}^{3}x + 1 . 5 \times {10}^{11}t\right)\overset{^}{j}T. The amplitude of the electric field would be

Options

  1. A6Vm−16{Vm}^{- 1} along xx-axis
  2. B3Vm−13{Vm}^{- 1} along zz-axis
  3. C6Vm−16{Vm}^{- 1} along zz-axis
  4. D2×10−8Vm−12 \times {10}^{- 8}{Vm}^{- 1} along zz-axis

Correct answer

C. 6Vm−16{Vm}^{- 1} along zz-axis

Step-by-step solution

The ratio of electric field amplitude to the magnetic field amplitude of an electromagnetic wave is equal to the speed of light in the medium. Therefore,

c=E0B0⇒E0=cB0c = \dfrac{{E}_{0}}{{B}_{0}} ⇒ {E}_{0} = c{B}_{0}

⇒E0=3×108×2×10−8⇒ {E}_{0} = 3 \times {10}^{8} \times 2 \times {10}^{- 8}

⇒E0=6Vm−1⇒ {E}_{0} = 6V{m}^{- 1}

According to the given equation B→=2×10−8sin\overset{\to}{B} = 2 \times {10}^{- 8}sin\left(0 . 5 \times {10}^{3}x + 1 . 5 \times {10}^{11}t\right)\overset{^}{j}Tthewavetravelsinthe wave travels inxdirection.Aselectricfieldandmagneticfieldvibrateperpendiculartothevelocityoflight,electricfieldcannotbealongdirection. As electric field and magnetic field vibrate perpendicular to the velocity of light, electric field can not be alongx axis.

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