The electromagnetic waves travel in a medium at a speed of $2.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · EM Waves

The electromagnetic waves travel in a medium at a speed of

2.0 \times 1 0^{8} m / s

. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

(A)2.25✓ Correct
(B)4.25
(C)6.25
(D)8.25

Answer: (A)

Solution

The speed of electromagnetic waves in a medium is given by

v = \frac{c}{μ _{r} ϵ _{r}}

, where

c = 3 \times 1 0^{8}

m/s is the speed of light in vacuum. Rearranging:

\frac{c}{v} = μ_{r} ϵ_{r}

. Substituting

v = 2 \times 1 0^{8}

m/s and

μ_{r} = 1.0

\frac{3 \times 1 0 ^{8}}{2 \times 1 0 ^{8}} = 1 \times ϵ_{r}

, so

\frac{3}{2} = ϵ_{r}

. Squaring both sides:

ϵ_{r} = \frac{9}{4} = 2.25

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option

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