Electromagnetic Waves

JEE Main level, single correct, medium

99 of 165

Question 99 of 165

A plane electromagnetic wave of frequency 25GHz25GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic filed is given by B⃗=5×10−8j^T.\vec{B}=5\times {10}^{-8} \hat{j} T. The corresponding electric field E⃗\vec{E} is (speed of light =3×108ms−1=3\times {10}^{8} m{s}^{-1} )

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Answer: (D) 15i^Vm15\hat{i}\dfrac{ V}{m}

Given, the electromagnetic wave is propagating in zz i.e., +k^+\hat{k} direction.
The relation between the magnitudes of electric field, magnetic field and the speed of light is given by
∣E∣∣B∣=C\dfrac{\left|E\right|}{\left|B\right|}=C
⇒∣E∣=∣B∣×C\Rightarrow \left|E\right|=\left|B\right|\times C
⇒∣E∣=5×10−8×3×108=15Vm−1\Rightarrow \left|E\right|=5\times {10}^{-8}\times 3\times {10}^{8}=15V{m}^{-1}
We know that the direction of propagation of electromagnetic wave is along E⃗×B⃗\vec{E}\times \vec{B}.
So, E⃗=15i^Vm−1\vec{E}=15\hat{i}V{m}^{-1}

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