Question

If the relative permeability of a medium is ${\mu }_r$ and its dielectric constant is ${\epsilon }_r$ then the velocity of light in that medium will be

• A. $\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}$
• B. $\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$
• C. $\sqrt{{\mu }_r{\epsilon }_r/{\mu }_{{\epsilon }_0}}$
• D. $\sqrt{{\mu }_0{\epsilon }_0/{\mu }_r{\epsilon }_r}$

Answer 1

Answer: (B)

$\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$

As we know that velocity of light is given by:

$c=\frac{1}{\sqrt{{ϵ}_0{\mu }_0}}$

If we change the medium then velocity is

$v=\frac{1}{\sqrt{ϵ\mu }}=\frac{1}{\sqrt{{ϵ}_0{ϵ}_r{\mu }_0{\mu }_r}}$

$=\frac{c}{\sqrt{{ϵ}_r{\mu }_r}}$