Question

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

• A. 25
• B. 15
• C. 81
• D. 10
• E. 6

Answer 1

Answer: (E)

Given refractive index $n=1.5$
Permeability ${\mu }_0=5\times {10}^{-7}H{m}^{-1}$ $n=\sqrt{{\mu }_r{\epsilon }_r}$ ${\epsilon }_r=\frac{n^2}{{\mu }_r}$ Or ${\epsilon }_r=\frac{n^2{\mu }_0}{\mu }$
$\left[\because {\mu }_r=\frac{\mu }{{\mu }_0}\right]$
Or ${\epsilon }_r=\frac{{(1.5)}^2\times 4\pi \times {10}^{-7}}{5\times {10}^{-7}}$ Or ${\epsilon }_r=6$