(a) Separate variables in cylindrical coordinates and find a general time-harmonic solution (,, z, t) of the...
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(a) Separate variables in cylindrical coordinates and find a general time-harmonic solution ψ(ρ,φ, z, t) of the scalar wave equation which propagates in the z-direction and remains finite on the z axis.
(b) Find the TE and TM electric and magnetic fields associated with the magnetic Hertz vector πm = ψ0 ẑ where ψ0 is the cylindrically symmetric solution found in part (a).
(c) Interpret ψ0(r, t) as a sumof planewaves exp[i(q · r − ωt)] where the q vectors have the same magnitude and are distributed uniformly on the surfaced of a cone.
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