What is the speed of a plane electromagnetic wave in a homogeneous, isotropic dielectric medium whose relative permittivity is ${\epsilon }_r=2.4$ and relative permeability is ${\mu }_r=1.3$?

Step-by-step solution

1. The speed of a wave in a dielectric is $v=\frac{c}{\sqrt{{\epsilon }_r{\mu }_r}}$, where $c=3.00\times 10^8\text{m/s}$.
2. Substitute ${\epsilon }_r=2.4$ and ${\mu }_r=1.3$ into the formula: $v=\frac{3.00\times 10^8}{\sqrt{2.4\times 1.3}}$.
3. Compute the product inside the square root: $2.4\times 1.3=3.12$.
4. Take the square root: $\sqrt{3.12}\approx 1.766$.
5. Divide the numerator by this result: $\frac{3.00\times 10^8}{1.766}\approx 1.70\times 10^8\text{m/s}$.

Concept tested: speed of EM wave in dielectric

Published 1 October 2026 · How this solution was prepared and checked