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Electromagnetic Induction

JEE Main level, single correct, medium

106 of 153

Question 106 of 153

The energy of an electromagnetic wave contained in a small volume oscillates with

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Answer: (A) Double the frequency of the wave

The formula to calculate the energy confined within the electric component of an electromagnetic wave can be written as

{u}_{E}=\dfrac{1}{2}{\epsilon }_{0}{E}^{2}dV...\left(1\right)

Let's assume that the equation of the electric component is given by

E={E}_{0}\sin \left(\omega t+\phi \right)...\left(2\right)

Substitute the expression for the electric field component from equation (2) into equation (1) and simplify to obtain the expression for the energy confined within the small volume

dV

\begin{matrix}{u}_{E} & = & \dfrac{1}{2}{\epsilon }_{0}{\left[{E}_{0}\sin \left(\omega t+\phi \right)\right]}^{2}dV \\ & = & \dfrac{1}{2}{\epsilon }_{0}{{E}_{0}}^{2}{\sin }^{2}\left(\omega t+\phi \right)dV \\ & = & \dfrac{1}{4}{\epsilon }_{0}{{E}_{0}}^{2}\left[1-\cos \left(2\omega t+2\phi \right)\right]...\left(3\right)\end{matrix}

From equation (3), it can be concluded that the frequency of oscillation of the energy confined within a small volume is double the frequency of the wave.

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JEE Main 2025 Apr 2 Shift 1 question paper

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