A plane EM wave travelling along z direction is described by and . Show that

(i) The average energy density of the wave is given by .


(ii) The time averaged intensity of the wave is given by .


In the electric field the energy density is given as,



In the magnetic field the energy density is given as,



Thus, total energy density is given as



The vector form of electric and magnetic field is given as,




The effective values of E2 and B2 over one cycle are their time average.


As we know,




Thus, average value of E2 is



average value of B2 is



Thus, time average of energy over one cycle is,




ii) As we know,



Where,


μ0=Absolute permeability


ε0=Absolute permittivity


Time average of energy density is given as,





Thus, it can be concluded as uB=uE





So average time intensity is,



1