Skin effect is a phenomenon where an alternating current tends to flow
and distribute itself along the surface layer or outside *skin* of a
conductor. This effect can for example be taken advantage of in power
transmission applications by layering inexpensive conductor materials
(for example aluminium) with a thin layer of more conductive material
(like copper). This model examines the skin effect in a
two-dimensional cross section of a thick circular wire with an outer
radius *R = 12 cm*.

A time-harmonic complex Helmholtz equation for the amplitude of the
electric field *E* is used to model the skin effect

*-∇·(1/µ∇E) + k*

^{2}E = 0where *mu* is the permeability *4π·10 ^{-7} H/m*, and
the wave number

*k*is given by

*k = sqrt(iωσ - ω*

^{2}ε)where *σ* is the conductivity of the material, *ε* the
dielectric properties, and *ω* angular frequency (here
*60 Hz*). Complex (and imaginary) numbers are denoted using the *i*
coefficient.