Due to presence of an em-wave whose electric component is given by E… | JEE Main 2025 (28 Jan, Shift 1)

Q4JEE Main 2025 · 28 JAN · SHIFT 1Medium

Energy Density & Intensity

Due to presence of an em-wave whose electric component is given by $E = 100 \sin(\omega t - kx)\text{ N C}^{-1}$ a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

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Answer: (c)

Energy $U = \tfrac{1}{2}\varepsilon_0 E_0^2 \times \pi r^2 L$
Half diameter $\Rightarrow$ area becomes $1/4$ , same $L$ .
Same $U \Rightarrow E_0^2$ must become 4 times $\Rightarrow E_0' = 2 \times 100 = 200$ N/C
So the answer is (c) $200 \sin(\omega t - kx)$ N C $^{-1}$ .

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