Consider electromagnetic waves in free space.
(a) Write the set of Maxwell’s equations for regions containing no free charge or current.
(b) Starting from these equations, derive the one–dimensional wave equation for the electric field component Ey(x,t) of a plane wave travelling along the x–axis.
(c) Obtain the corresponding wave equation for the magnetic field component Bz(x,t).
(d) Show that the phase velocity of the wave is c=1/μ0ε0.
(e) Hence prove that the ratio of the peak amplitudes of the electric and magnetic fields satisfies E0=cB0.