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

## Abstract

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{sub z}(r,z)] and radial [E{sub 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 r{sub 0} and thickness t{sub 0}) and contact radius of the electrode (r{sub c}) has been investigated by varying them in a systematic fashion. The skin-effect behavior at high frequenciesmore »

- Authors:

- School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

- Publication Date:

- OSTI Identifier:
- 20982710

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 101; Journal Issue: 4; Other Information: DOI: 10.1063/1.2405734; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; BESSEL FUNCTIONS; COMPUTERIZED SIMULATION; ELECTRIC CURRENTS; ELECTRIC FIELDS; ELECTRIC IMPEDANCE; ELECTRODES; FINITE ELEMENT METHOD; MAXWELL EQUATIONS; SKIN EFFECT; THICKNESS

### Citation Formats

```
Kelekanjeri, V. Siva Kumar G., and Gerhardt, Rosario A..
```*Electric field distribution within a metallic cylindrical specimen for the case of an ideal two-probe impedance measurement*. United States: N. p., 2007.
Web. doi:10.1063/1.2405734.

```
Kelekanjeri, V. Siva Kumar G., & Gerhardt, Rosario A..
```*Electric field distribution within a metallic cylindrical specimen for the case of an ideal two-probe impedance measurement*. United States. doi:10.1063/1.2405734.

```
Kelekanjeri, V. Siva Kumar G., and Gerhardt, Rosario A.. Thu .
"Electric field distribution within a metallic cylindrical specimen for the case of an ideal two-probe impedance measurement". United States.
doi:10.1063/1.2405734.
```

```
@article{osti_20982710,
```

title = {Electric field distribution within a metallic cylindrical specimen for the case of an ideal two-probe impedance measurement},

author = {Kelekanjeri, V. Siva Kumar G. and Gerhardt, Rosario A.},

abstractNote = {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{sub z}(r,z)] and radial [E{sub 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 r{sub 0} and thickness t{sub 0}) and contact radius of the electrode (r{sub 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 (r{sub 0},t{sub 0}) and is independent of the contact radius of the electrodes (r{sub c}). The constriction behavior, however, is predominantly governed by r{sub c}, although it depends on all three geometric parameters. Lastly, the idea of a limiting thickness (t{sub 0,lim}) and a limiting field profile (E{sub z,lim}|{sub z=t{sub 0},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 t{sub 0}, while the semi-infinite solution is only valid for large values of t{sub 0}.},

doi = {10.1063/1.2405734},

journal = {Journal of Applied Physics},

number = 4,

volume = 101,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}