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Surface currents

A surface current can be regarded as the limiting case when a finite amount of current

I flows as shown in Figurę 6.2 in a thin slab of area dimensions a and b and thickness t

While t is smali but not zero we may describe this situation in terms of a volume

current density J or a surface current density K. We may relate the magnituds of these

quantities to I by I = Ka= Jat. (6.5)

If the materiał has electric resistivity p(note this symbol does not for the moment

represent volume charge density) the resistance of the slab is R = pb at

. (6.6)

The power P = bR dissipated in the slab is therefore given by P =

«2a2bp

at

(6.7)

i.e.

P =

łOabp

t

• (6.8)

If K and parę non-zero, i.e. we have a surface current and the conductor is not perfect,

then P ->°o as t -> 0. Since we cannot produce an infinite amount of power we must

have K = 0_; i.e. we cannot have a surface current density in an imperfect conductor.