2.3 Energy density of electromagnetic waves

1.1 Displacement current
1.3 Maxwell's equations

2.1 Properties of electromagnetic waves
2.2 Production of electromagnetic waves
2.3 Energy density of electromagnetic waves
2.4 Intensity of electromagnetic waves
2.5 Momentum of electromagnetic waves
2.6 Radiation pressure
2.7 Poynting vector
2.8 Electromagnetic spectrum

Electromagnetic waves carry energy as they travel through space and this energy is equally shared by electric field and magnetic field of electromagnetic wave.

The energy density of the electric field is, $${\mu _E} = \frac{1}{2}{\varepsilon _0}{E^2}$$

The energy density of the magnetic field is, $${\mu _B} = \frac{1}{2}\frac{{{B^2}}}{{{\mu _0}}}$$

Average density of the electric field is, $${\mu _{{E_{Avg}}}} = \frac{1}{4}{\varepsilon _0}E_0^2$$

Average density of the magnetic field is, $${\mu _{{B_{Avg}}}} = \frac{1}{4}\frac{{B_0^2}}{{{\mu _0}}}$$ or $${\mu _{{B_{Avg}}}} = \frac{1}{4}{\varepsilon _0}E_0^2$$

Average energy density of electromagnetic wave is, $$\begin{equation} \begin{aligned} {\mu _{Avg}} = {u_{{E_{Avg}}}} + {u_{{B_{Avg}}}} \\ {\mu _{Avg}} = \frac{1}{4}{\varepsilon _0}E_0^2 + \frac{1}{4}{\varepsilon _0}E_0^2 \\ {\mu _{Avg}} = \frac{1}{2}{\varepsilon _0}E_0^2 \\\end{aligned} \end{equation} $$