Abstract
We demand that the Gauss law at the edge must be obeyed by the electric potential ϕ(r) generated within a neutral plasma/electrolyte of strictly finite size by the introduction of a test charge q b . Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of ϕ(r) is guaranteed at short-distance, and accumulation of induced charges near the centre and the surface can be demonstrated rigorously. In contrast, the standard Debye-Hückel potential ϕ D(r) applicable to unbounded plasma has the strange features that the Gauss law cannot be obeyed at the plasma’s edge, total ionic numbers themselves are altered, the short-distance Coulomb behaviour has to be imposed by hand, and induced charge appearance at the surface cannot be built-in.
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Dubey, R.K., Menon, V.J., Mishra, M. et al. Gauss law constraints on Debye-Hückel screening. Pramana - J Phys 69, 423–433 (2007). https://doi.org/10.1007/s12043-007-0143-0
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DOI: https://doi.org/10.1007/s12043-007-0143-0