In a sourceless medium in which J=0 and ρv=0,assume a rectangular coordinate system in which E and H arefunctions only of z and t. The medium has permittivity ε andpermeability μ.
(a) If E=Exax andH=Hyay, begin with Maxwell's equations and determine the second order partial differential equation that Ex must satisfy.
(b) Show that Ex=E0 cos (ωt-βz) isa solution of that equation for a particular value of β.
(c) Find β as a function of given parameters.