2.0 Electromagnetic Waves

For a plane progressive electromagnetic wave propagating along the $+z$ direction, the electric and magnetic fields can be written as, $$\begin{equation} \begin{aligned} E = {E_0}\sin \left( {kz - \omega t} \right) \\ B = {B_0}\sin \left( {kz - \omega t} \right) \\\end{aligned} \end{equation} $$

In electromagnetic wave, the electric and magnetic fields vary with space and time and have the same frequency and are in the same phase.

The amplitudes of electric and magnetic fields in free space, in electromagnetic waves are related by,

$${E_0} = c{B_0}\quad {\text{or}}\quad {B_0} = \frac{{{E_0}}}{c}$$

The speed of electromagnetic wave in free space is, $$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}$$

where,

${{\mu _0}}$: Permeability of free space

${{\varepsilon _0}}$: Permittivity of free space

The speed of electromagnetic wave in a medium is, $$v = \frac{1}{{\sqrt {\mu \varepsilon } }}$$

${{\mu}}$: Permeability of the medium

${{\varepsilon}}$: Permittivity of the medium

As we know, $$\mu = {\mu _0}{\mu _r}$$$$\varepsilon = {\varepsilon _0}{\varepsilon _r}$$

So, we can write, $$v = \frac{1}{{\sqrt {{\mu _0}{\mu _r}{\varepsilon _0}{\varepsilon _r}} }}{\text{ }}$$$$v = \frac{c}{{\sqrt {{\mu _r}{\varepsilon _r}} }}$$