An electromagnetic wave is propagating in a medium with permittivity $ϵ$ and permeability $\mu$. The speed $v$ of the wave in this medium is:

Solution

1. Maxwell's equations in a medium lead to the wave equation for the electric field.
2. The wave equation is ${\nabla }^{2}E=\mu ϵ\frac{{\partial }^{2}E}{\partial t^2}$.
3. Comparing this to the standard wave equation ${\nabla }^{2}E=\frac{1}{v^2}\frac{{\partial }^{2}E}{\partial t^2}$, we identify $\frac{1}{v^2}=\mu ϵ$.
4. Solving for $v$ gives $v=\frac{1}{\sqrt{\mu ϵ}}$.
5. Hence the answer is (B).