The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, E y =20 sin (3 × 10 6 x -4.5 × 10 14 t ) V / m (where x , t and other values have S.I. units). The dielectric constant of the medium is (speed of light in free space is 3 × 10 8 m / s )

Physics · Electromagnetic Waves

JEE Main 2026 — 22 January, Morning Shift — Question 45

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $\mathrm{E}_{\mathrm{y}}=20 \sin \left(3 \times 10^{6} \mathrm{x}-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m}$ (where $\mathrm{x}, \mathrm{t}$ and other values have S.I. units). The dielectric constant of the medium is (speed of light in free space is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )

Answer: 4

Numerical answer — enter this value.

Step-by-step solution

$n=\frac{C}{V}$ $\mathrm{V}=\frac{\omega}{\mathrm{k}}=\frac{4.5 \times 10^{14}}{3 \times 10^{6}}=\frac{3}{2} \times 10^{8}$ $\mathrm{n}=2$ $\mathrm{n}=\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}} \left(\mu_{\mathrm{r}}=1\right)$ $2=\sqrt{\varepsilon_{\mathrm{r}}}$ $\varepsilon_{\mathrm{r}}=4$ $\mathrm{m}_{1}=\pi \mathrm{R}_{1}^{2} \mathrm{~T}_{1} \rho$ $\mathrm{I}_{1}=\frac{\mathrm{m}_{1} \mathrm{R}_{1}^{2}}{2}$

\mathrm{m}_{2}=\pi \mathrm{R}_{2}^{2} \mathrm{~T}_{2} \rho

$\mathrm{I}_{2}=\frac{\mathrm{m}_{2} \mathrm{R}_{2}^{2}}{2}$

\frac{\pi \mathrm{R}_{1}^{2} \mathrm{~T}_{1} \rho \mathrm{R}_{1}^{2}}{2}=\frac{\pi \mathrm{R}_{2}^{2} \mathrm{~T}_{2} \rho \mathrm{R}_{2}^{2}}{2} \Rightarrow \frac{\mathrm{~T}_{1}}{\mathrm{~T}_{2}}=\frac{1}{16}

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 22 January, Morning Shift
Subject: Physics
Chapter: Electromagnetic Waves
Topic: Properties of EM Waves and Electromagnetic Spectrum