Explanation: Let us assume the wave travels in z direction so the

electric and magnetic fields of the wave are given by

Their average values over one cycle would be the average from time

t=0 to t=T.

Average of electric field

(because and )

Therefore, the average of electric field is zero.

Similarly average of magnetic field is also zero as

So electric and magnetic field have their average value zero.

Now the electric energy associated with the electric field is given by

…(i)

where ϵ₀ is the electric permittivity of free space(vacuum) and is

equal to 8.85 × 10^-12 C² N^-1 m^-2 and U_de is the energy density of

electric field.

Similarly, the magnetic energy associated with the magnetic field is

given by

…(ii)

where μ₀ is the magnetic permeability of free space and its value is

4π × 10^-7 T m A^-1, U_db is the magnetic field energy density.

Also the amplitudes of electric and magnetic fields are related as

…(iii)

where C is the speed of light in vacuum.

and

Using (iii) in (i)

…. (iv)

The electrical permittivity and magnetic permeability of free space

related as

…. (v)

Using (v) in (iv)

Therefore, the electric and magnetic energy densities are same in

magnitude and so their average values will be same.

Average of electric energy over one cycle will be

So electric and magnetic energy and have non zero average values.