In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of and amplitude . Show that the average energy density of the field equals the average energy density of the B field.

Frequency of the electromagnetic wave is given as

Electric field amplitude is given as

Speed of light is known as

Energy density of the electric field is represented as,

And, energy density of the magnetic field is given as:

Where,

is the permittivity of free space

is the permeability of free space

…(1)

Now,

On putting equation (2) in equation (1), we get

On squaring on both sides, we get