Surface currents - wykład

Surface currents A surface current can be regarded as the limiting case when a finite amount of current
I flows as shown in Figure 6.2 in a thin slab of area dimensions a and b and thickness t
While t is small 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 material has electric resistivity ρ (note this symbol does not for the moment
represent volume charge density) the resistance of the slab is
R =
ρ b
at
. (6.6)
The power P = I2R dissipated in the slab is therefore given by
P =
K2a2bρ
at
(6.7)
i.e.
P =
K2abρ
t
. (6.8)
If K and ρ are non-zero, i.e. we have a surface current and the conductor is not perfect,
then P →∞ 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.
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