Consider a parallel-plate capacitor with circular plates of radius a separated by a distance 2L.

A paper published in 1983 proposed a solution for the potential for this situation of the form

Where J₀ is the zero-order Bessel function and

(a) Find the function f (k, z) so the proposed solution satisfies the boundary conditions on the surfaces of the plates. You may make use of the integral

(b) Show that the proposed solution nevertheless fails to solve the problem because the electric field it predicts is not a continuous function of z when ρ > a

T 2L I Z +V -V -a- P