# The 3-dimensional Helmholtz equation for the scalar potential V inside the coaxial waveguide… 1 answer below »

( 12 pts.) 6) The 3-dimensional Helmholtz equation for the scalar potential V inside the coaxial waveguide shown at right is given by:

V2V +k2V = 0

where k is a constant related to the wave number of the air inside the waveguide. Assume the potential is zero on the outer surface of the inner conductor of radius a, and on the inner surface of the outer conductor of radius b. Find the eigenvalues and the eigenfunctions of V. (For the eigenvalues, find an equation that its solutions are the eigenvalues)

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