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NEET 2019
Exam
NEET
Year
2019
Subject
Physics
Chapter
Electromagnetic Waves

NEET 2019 · Physics · Electromagnetic Waves

For a transparent medium relative permeability and permittivity μ_...

For a transparent medium relative permeability and permittivity μr\mu_{\mathrm{r}} and ϵr\epsilon_{\mathrm{r}} are 1.0 and 1.44 respectively. The velocity of light in this medium would be

Options

  1. A2.5×108 m/s2.5 \times 10^8 \mathrm{~m} / \mathrm{s}
  2. B3×108 m/s3 \times 10^8 \mathrm{~m} / \mathrm{s}
  3. C2.08×108 m/s2.08 \times 10^8 \mathrm{~m} / \mathrm{s}
  4. D4.32×108 m/s4.32 \times 10^8 \mathrm{~m} / \mathrm{s}

Correct answer

A. 2.5×108 m/s2.5 \times 10^8 \mathrm{~m} / \mathrm{s}

Step-by-step solution

The speed of any electromagnetic wave (EM) like light in any medium of permeability, μ\mu and permittivity, ε\varepsilon is given by v=1με\mathrm{v}=\frac{1}{\sqrt{\mu \varepsilon}} Also, μ=μ0μr\mu=\mu_0 \mu_r and ε=ε0εr\varepsilon=\varepsilon_0 \varepsilon_r where, μ0\mu_0 and ε0\varepsilon_0 are permeability and permittivity in free space and μr\mu_{\mathrm{r}} and εr\varepsilon_{\mathrm{r}} are relative permeability and relative permittivity of medium respectively. Here, μr=1.0\mu_{\mathrm{r}}=1.0 εr=1.44\varepsilon_{\mathrm{r}}=1.44\begin{aligned} \therefore \quad \quad \quad \mathrm{v} & =\frac{1}{\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}} \mu_0 \varepsilon_0}}=\frac{\mathrm{c}}{\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}} \quad\left[\because \mathrm{c}=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\right] \\ & =\frac{3 \times 10^8}{\sqrt{1 \times 1.44}} \\ & =2.5 \times 10^8 \mathrm{~ms}^{-1} \end{aligned}
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