Solveeit Logo
Login

Question

Question: The refractive index and permeability of a medium are 1.5 and 5×\(10^{- 7}\)H \(m^{- 1}\)respectivel...

The refractive index and permeability of a medium are 1.5 and 5×10−710^{- 7}H m−1m^{- 1}respectively. The relative permittivity of the medium is nearly:

A

25

B

15

C

10

D

6

Answer

6

Explanation

Solution

: Refractive index, ,n=cvn = \frac{c}{v}

or v=cn=3×1081.5=2×108ms−1v = \frac{c}{n} = \frac{3 \times 10^{8}}{1.5} = 2 \times 10^{8}ms^{- 1}

Here, μ=5×10−7Nm−1\mu = 5 \times 10^{- 7}Nm^{- 1}

∴v=1με=1με0εr\therefore v = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{1}{\sqrt{\mu\varepsilon_{0}\varepsilon_{r}}}

εr=1v2με0=1(2×108)2×(5×10−7)×(8.85×10−12)\varepsilon_{r} = \frac{1}{v^{2}\mu\varepsilon_{0}} = \frac{1}{(2 \times 10^{8})^{2} \times (5 \times 10^{- 7}) \times (8.85 \times 10^{- 12})}

=5.65≃6= 5.65 \simeq 6 =5.65≃6= 5.65 \simeq 6