Question

The refractive index and permeability of medium are $1.5$ and $5\times {10}^{-7}H{m}^{-1}$ respectively. The relative permittivity of the medium is nearly

• A. $2.51$
• B. $15$
• C. $10$
• D. $6$

Answer 1

Answer: (A)

$2.51$

Given,

$n=1.5$

$c=3\times {10}^{8}m/s$

$\mu =5\times {10}^{-7}H/m$

Speed of light through medium,

$v=\frac{c}{n}$

$v=\frac{3\times {10}^8}{1.5}=2\times {10}^{8}m/s$

Velocity of light in medium,

$c=\frac{1}{\sqrt{\epsilon \mu }}$

$c^2=\frac{1}{\mu \epsilon }$

$\epsilon =\frac{1}{c^2\mu }$

$\epsilon =\frac{1}{3\times 3\times {10}^8\times {10}^8\times 5\times {10}^{-7}}$

$\epsilon =0.022\times {10}^{-9}F/m$

Relative permitivity,

${\epsilon }_r=\frac{\epsilon }{{\epsilon }_0}$

${\epsilon }_r=\frac{0.22\times {10}^{-9}}{8.85\times {10}^{-12}}$

${\epsilon }_r=2.51$