The magnetic field in a plane electromagnetic wave is given by

B = (200 μT) sin [(4.0 × 10¹⁵ s^–1) (t –x/c)].

Find the maximum electric field and the average energy density corresponding to the electric field.

Given: The equation of magnetic field of a plane electromagnetic

wave

B = (200 μT) sin [(4.0 × 10¹⁵ s^–1) (t –x/c)]

where the amplitude of magnetic field is .

The amplitude of the electric field is related with amplitude of

magnetic field as

where C is the speed of light in free space and E₀ is the amplitude

of electric field.

Thus the electric field intensity is given as

The energy density associated with an electric field is given as

where U_d is the energy density, ϵ₀ is the electric permittivity of free space(vacuum) and is equal to 8.85 × 10^-12 C² N^-1 m^{-2 and} E₀ is the amplitude of electric field.

Thus the electric field energy density is given by

The maximum electric field is and the corresponding

electric field energy density is .