Electromagnetic Waves

JEE Main level, single correct, medium

40 of 165

Question 40 of 165

A plane electromagnetic wave of frequency 35MHz35MHz travels in free space along the XX-direction. At a particular point (in space and time) E⃗=9.6j^Vm−1\vec{E}=9.6\hat{j}V{m}^{-1}. The value of magnetic field at this point is:

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Answer: (A) 3.2×10−8k^T3.2\times {10}^{-8}\hat{k}T

At every instant, the ratio of the magnitude of the electric field to the magnitude of the magnetic field in an electromagnetic wave equals the speed of light.
Therefore, EB=c\dfrac{E}{B}=c
⇒EB=3×108\Rightarrow \dfrac{E}{B}=3\times {10}^{8}
⇒B=E3×108=9.63×108\Rightarrow B=\dfrac{E}{3\times {10}^{8}}=\dfrac{9.6}{3\times {10}^{8}}
⇒B=3.2×10−8T\Rightarrow B=3.2\times {10}^{-8}T
Now, direction of magnetic field can be calculated as
B^=v^×E^\hat{B}=\hat{v}\times \hat{E}
=i^×j^=k^=\hat{i}\times \hat{j}=\hat{k}
So, B⃗=3.2×10−8k^T\vec{B}=3.2\times {10}^{-8}\hat{k}T

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