Question

If $c$ is the speed of electromagnetic waves in vacuum, its speed $v$ in a medium of dielectric constant $K$ and relative permeability ${\mu }_r$ is (c is the speed of light)

• A. $v=\frac{1}{\sqrt{{\mu }_{r}K}}$
• B. $v=c\sqrt{{\mu }_{r}K}$
• C. $v=\frac{c}{\sqrt{{\mu }_{r}K}}$
• D. $v=\frac{K}{\sqrt{{\mu }_{r}c}}$

Answer 1

Answer: (C)

Speed of light in vacuum, $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
and in another medium $v=\frac{1}{\sqrt{\mu \epsilon }}$
$\therefore \frac{c}{v}=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}=\sqrt{{\mu }_{r}K}$
$\Rightarrow v=\frac{c}{\sqrt{{\mu }_{r}K}}$