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Unlike an ohmic conductor, the resistance of an arc decreases as the current increases.
They typically have non-linear current-voltage characteristics, and do not behave as simple ohmic conductors.
The shell is assumed to be an isotropic ohmic conductor; the fields are described by Poisson's equation.
The ionosphere is an ohmic conductor, so some consider that such currents require a driving voltage, which an, as yet unspecified, dynamo mechanism can supply.
In terms of the basic properties of the right-cylindrical current-carrying metallic ohmic conductor, where the charge-carriers are electrons, this expression can be rewritten as :