A plane electromagnetic wave travels in a medium of relative… | JEE Main 2022 (24 Jun, Shift 1)

Q15JEE Main 2022 · 24 JUN · SHIFT 1Difficult

Speed of EM Waves in a Medium

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 $\times$ 10 $-$ 2 Am ${}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point?

(Given: Permeability of free space $\mu$ 0 = 4 $\pi \times$ 10 $-$ 7 NA ${}^{-2}$ , speed of light in vacuum c = 3 $\times$ 108 ms ${}^{-1}$ )

Show answer and solution

Answer: (c)

$\dfrac{E}{H} = \sqrt{\dfrac{\mu}{\varepsilon}} = \sqrt{\dfrac{\mu_0}{\varepsilon_0}}\sqrt{\dfrac{\mu_r}{\varepsilon_r}}$ , with $\sqrt{\mu_0/\varepsilon_0} = \mu_0 c = 120\pi \approx 377\ \Omega$
$\sqrt{\dfrac{1.61}{6.44}} = \sqrt{0.25} = 0.5 \Rightarrow E/H = 60\pi \approx 188.5\ \Omega$
$E = 188.5 \times 4.5 \times 10^{-2} \approx 8.48$ V/m
So the answer is (c) 8.48 V m $^{-1}$ .

Report a mistake

Speed of EM Waves in a Medium question from JEE Main 2022 (24 Jun, Shift 1)

More questions on Speed of EM Waves in a Medium