Derive the expression for the speed $v$ of an electromagnetic wave in a homogeneous, isotropic dielectric medium having relative permittivity ${\epsilon }_r$ and relative permeability ${\mu }_r$. Then calculate $v$ for ${\epsilon }_r=2.5$ and ${\mu }_r=1.2$.

Step-by-step solution

1. In any medium the wave speed is $v=\frac{1}{\sqrt{\mu \epsilon }}$, where $\mu ={\mu }_0{\mu }_r$ and $\epsilon ={\epsilon }_0{\epsilon }_r$.
2. Substituting $\mu$ and $\epsilon$ gives $v=\frac{1}{\sqrt{{\mu }_0{\mu }_r{\epsilon }_0{\epsilon }_r}}=\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$, because $c=1/\sqrt{{\mu }_0{\epsilon }_0}$.
3. Now insert the given values: ${\mu }_r=1.2$, ${\epsilon }_r=2.5$.
4. Compute the product ${\mu }_r{\epsilon }_r=1.2\times 2.5=3.0$.
5. Take the square root: $\sqrt{3.0}=1.732$.
6. Finally, $v=\frac{c}{1.732}=\frac{3.0\times 10^8}{1.732}=1.734\times 10^8{\text{m s}}^{-1}$, which is written as $1.73\times 10^8{\text{m s}}^{-1}$.

Concept tested: Wave speed in a dielectric medium

Published 17 September 2026 · How this solution was prepared and checked