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

The Correct Option is C

\(\mu_{0}\) 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): \(\sqrt{\frac{\mu \varepsilon }{{{\mu }_{o}}{{\varepsilon }_{o}}}}\)