Electric polarizability for a thick eccentric annular aperture with a floating inner conductor

An electrostatic potential penetration into an eccentric annular aperture in a thick conducting plane is investigated when an inner conductor is electrically floating. Conformal mapping is used to transform an eccentric annular aperture into a concentric aperture. The Hankel-transform and eigenfunction expansion is utilized to solve the boundary-value problem for a concentric annular aperture. Computation is performed to illustrate the electric polarizability, capacitance, and potential distribution for various aperture geometries.