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}}{{\varepsilon }_{r}}} $ $ {{\varepsilon }_{r}}=\frac{{{n}^{2}}}{{{\mu }_{r}}} $ Or $ {{\varepsilon }_{r}}=\frac{{{n}^{2}}{{\mu }_{0}}}{\mu } $
$ \left[ \because {{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}} \right] $
Or $ {{\varepsilon }_{r}}=\frac{{{(1.5)}^{2}}\times 4\pi \times {{10}^{-7}}}{5\times {{10}^{-7}}} $ Or $ {{\varepsilon }_{r}}=6 $