A plane electromagnetic wave travelling in the +x-direction in vacuum has an electric field of the form
E(x,t)=E0j^sin(kx−ωt).
(i) Prove that the associated magnetic field may be written as B(x,t)=B0k^sin(kx−ωt) and obtain the relation E0=cB0.
(ii) Determine the instantaneous energy densities uE and uB of the electric and magnetic fields and show that they are equal at every point in space and time.
(iii) Using your results, find an expression for the magnitude of the time-averaged energy flux (Poynting vector) carried by the wave in terms of ε0, E0 and c."