About the effects of diffusion in electric tomography

TL;DR

This paper derives exact and approximate solutions for electric and magnetic fields in diffusive media, revealing how diffusion influences electric monopole detection and magnetic field independence in electric tomography.

Contribution

It provides closed-form and approximate solutions for fields in diffusive media, clarifying the role of diffusion effects and monopole signals in electric tomography.

Findings

Diffusion effects lead to Yukawa-like potentials in electric fields.

Magnetic field signals are unaffected by diffusion.

Detection of electric monopoles is feasible at specific frequencies.

Abstract

The Maxwell equations for an homogeneous medium in which electric currents are composed of Ohmic, diffusive and impressed currents are written in the static approximation in which displacements currents are neglected. Closed exact expressions are given for the solutions of the charge density, electric field potential and the magnetic field intensity as functions of the impressed currents and densities. Also, approximate formulae for these magnitudes are derived. The solutions correctly reproduce the conclusions of a previous work in which the relevance of Yukawa like potentials determined by diffusion effects were identified. Within the approximate solutions, the effective potential generated by the impressed sources is given by the superposition of Yukawa potentials created by the impressed charges concentrated in a given volume element. This representation makes evident that at small spatial regions, the experimental detectors are able to measure spherically symmetrical signals, indicating the presence of electric monopoles. The discussion also allows to argue that the magnetic field tomographic signal becomes completely independent of the presence of diffusion in the medium. The analysis also permits to determine the range of space and temporal frequencies in which the diffusion effects might become important in justifying the detection of monopole signals.