Consider a harmonic electromagnetic plane wave with angularfrequency ω and propagation vector k=(kx,ky,kz) (i.e., propagatingin an arbitrary direction). The electric field vector isE=(Ex,Ey,Ez) with amplitudes (Exo,Eyo,Ezo) and the magnetic fieldvector is B=(Bx,By,Bz) with amplitudes (Bxo,Byo,Bzo).
a) Write an expression for the electric and magnetic waves usingcomplex representation.
b) Using the laws of electromagnetism without sources (Maxwell’sequations in free space), prove that k × E = ωB, and k · E =0
c) What does part b) tell you about the relative directions of k, Eand B?
