A plane EM wave travelling along z-direction is described by$\overrightarrow{\mathrm{E}}={\mathrm{E}}_0<mspace\; width="1em"></mspace>\sin (\mathrm{kz}-\mathrm{\omega t})\hat{\mathrm{i}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}={\mathrm{B}}_0<mspace\; width="1em"></mspace>\sin (\mathrm{kz}-\mathrm{\omega t})\hat{\mathrm{j}}.<mspace\; width="1em"></mspace>\mathrm{Show}<mspace\; width="1em"></mspace>\mathrm{that}:$

(i) the average energy density of the wave is given by \(U_{av}=\frac14\varepsilon_0E^2_0+\frac14\frac{B^2_0}{\mu_0}\)

(ii) the time averaged intensity of the wave is given by \(I_{av}=\frac12c\varepsilon_0E^2_0\).