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JEE Main 20207 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2020 · 7 January · Morning Shift · Physics · Electromagnetic Waves

If the magnetic field in a plane electromagnetic wave is given by →...

If the magnetic field in a plane electromagnetic wave is given by $\overset{\to}{B} = 3 \times {10}^{- 8}\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{j}T, then what will be expression for electric field ?

Options

  1. A\overset{\to}{E} = \left(60\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{k}\dfrac{V}{m}\right)
  2. B\overset{\to}{E} = \left(9\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{k}\dfrac{V}{m}\right)
  3. C\overset{\to}{E} = \left(3 \times {10}^{- 8}\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{j}\dfrac{V}{m}\right)
  4. D\overset{\to}{E} = \left(3 \times {10}^{- 8}\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{i}\dfrac{V}{m}\right)

Correct answer

B. \overset{\to}{E} = \left(9\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{k}\dfrac{V}{m}\right)

Step-by-step solution

E0B0=C\dfrac{{E}_{0}}{{B}_{0}} = C (speed of light in vacuum)
E0=B0C=3×10−8×3×108{E}_{0} = {B}_{0}C = 3 \times {10}^{- 8} \times 3 \times {10}^{8}
=9NC= 9\dfrac{N}{C}
So,

E=9sin⁡(\omegat+kx+ϕ)E = 9\sin \left(\omegat + kx + ϕ\right)

\overset{\to}{E} = \left(9\sin \left(1.6 \times {10}^{3}x + 48 \times {10}^{10}t\right)\overset{^}{k}\dfrac{V}{m}\right)

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