Question

If c is the speed of electromagnetic waves in vacuum, its speed in a medium of dielectric constant k and relative permeability ${\mu }_{r}is$

• 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

The correct option is C $v=\frac{c}{\sqrt{{\mu }_{r}k}}$

Speed of light of vacuum $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}.....\left(1\right)$

And in another medium $v=\frac{1}{\sqrt{\mu v}}...\left(2\right)$

$\mu r=\frac{\mu }{{\mu }_0},{ϵ}_r=\frac{ϵ}{{ϵ}_0}=k$

Dividing by equation $\left(1\right)$&$\left(2\right)$

$\frac{c}{v}=\frac{\sqrt{\mu ϵ}}{\sqrt{{ϵ}_0{\mu }_0}}$

$=\sqrt{\left(\frac{\mu }{{\mu }_0}\right)}\frac{ϵ}{{ϵ}_0}=\sqrt{{\mu }_{r}k}$

$\frac{c}{v}=\sqrt{{\mu }_{r}k}$

$v=\frac{c}{\sqrt{{\mu }_{r}k}}$