Question

The electrical permittivity and magnetic permeability of free space are respectively ${{\varepsilon }_{o}}$ and ${{\mu }_{0}}$ . The corresponding value for a medium is:

• A. $\sqrt{\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{\mu \varepsilon }}$
• B. ${{\left( \frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{\mu \varepsilon } \right)}^{3/2}}$
• C. $\sqrt{\frac{\mu \varepsilon }{{{\mu }_{o}}{{\varepsilon }_{o}}}}$
• D. $\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{\mu \varepsilon }$

Answer 1

Answer: (C)

$\sqrt{\frac{\mu \varepsilon }{{{\mu }_{o}}{{\varepsilon }_{o}}}}$

Answer 2

$\mu_{0}$ is called permeability of free space and $\varepsilon_{0}$ is called permittivity of free space.
From Huygens wave theory $n=\frac{\text { speed of light in vacuum }(c)}{\text { speed of light in medium (v) }}$
Since, $c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}, v=\frac{1}{\mu \varepsilon} .$
$\therefore n=\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}$

So, the correct option is (C): $\sqrt{\frac{\mu \varepsilon }{{{\mu }_{o}}{{\varepsilon }_{o}}}}$