An electromagnetic wave travels in a homogeneous, isotropic dielectric medium whose relative permittivity is ${\epsilon }_r=3.0$ and relative permeability is ${\mu }_r=1.1$. The wave frequency is $f=6.0\times 10^{14}\text{Hz}$. (i) Find the speed $v$ of the wave in the medium. (ii) Find its wavelength $\lambda$ in the medium.

Step-by-step solution

1. Write the absolute permittivity $\epsilon ={\epsilon }_0{\epsilon }_r$ and absolute permeability $\mu ={\mu }_0{\mu }_r$.
2. The speed of an EM wave in a medium is $v=\frac{1}{\sqrt{\mu \epsilon }}$. Substitute $\epsilon$ and $\mu$ : $v=\frac{1}{\sqrt{{\mu }_0{\mu }_r{\epsilon }_0{\epsilon }_r}}=\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$ where $c=3.00\times 10^8{\text{m s}}^{-1}$.
3. Calculate $\sqrt{{\mu }_r{\epsilon }_r}=\sqrt{1.1\times 3.0}=\sqrt{3.3}=1.817$. Hence $v=\frac{3.00\times 10^8}{1.817}=2.50\times 10^8{\text{m s}}^{-1}$.
4. The wavelength in the medium is $\lambda =\frac{v}{f}=\frac{2.50\times 10^8}{6.0\times 10^{14}}=4.17\times 10^{-7}\text{m}$.

Concept tested: speed of EM wave in dielectric

Published 20 September 2026 · How this solution was prepared and checked