Electric field distribution within a metallic cylindrical specimen for the case of an ideal two-probe impedance measurement.

A closed form analytical solution for the electric field distribution inside a metallic cylindrical disk specimen has been derived for the problem of a two-probe impedance measurement. A two-probe impedance measurement can be treated as current injection and extraction by means of source and sink electrodes that are placed on opposite sides of a specimen. The analytical formulation is based on Maxwell’s equations for conductors and the derivation has been conducted on the premise of continuum considerations within the specimen. The derived field expressions for axial [E_z(r,z)] and radial [E_r(r,z)] fields are expressed in terms of Bessel series. As an extension to this problem, a semi-infinite solution is also given for the case of an infinitely long cylinder. The analytical solutions thus derived have been verified by computer simulations using a commercially available finite element package. The electric field distributions inside the specimen obtained via analytical and finite element solutions are in excellent agreement with each other. The dependence of skin-effect and constriction behaviors on specimen geometry (radius r₀ and thickness t₀) and contact radius of the electrode (r_c) has been investigated by varying them in a systematic fashion. The skin-effect behavior at high frequencies is strictly a function of the dimensions of the disk (r₀,t₀) and is independent of the contact radius of the electrodes (r_c). The constriction behavior, however, is predominantly governed by r_c, although it depends on all three geometric parameters. Lastly, the idea of a limiting thickness (t_0,lim) and a limiting field profile ( E_z,lim|_z=t0,lim/2) is discussed so as to determine the range of applicability of the analytical solutions. The analytical solution derived for the disk shows good agreement with the finite element solutions for all values of t₀, while the semi-infinite solution is only valid for large values of t₀. [ABSTRACT FROM AUTHOR]