Details

Snapshot 1: the skin depth of copper is about 200 μm in a 0.1 MHz field

Snapshot 2: the high permeance of iron contributes to decreasing the diffusing distance

Snapshot 3: brine, a poor conductor, still retains screening effects to lengths of the order of meters

The electromagnetic fields in a conductor are governed by the diffusion equation, in which the skin depth is given by . The values for copper and iron are much smaller than for brine. The fields, a function of space and time, are expressed as

,

,

.

The maximum values are related by , , , where the amplitude of the applied field is set equal to . Those values are shown in the table at the bottom. For copper and brine, the maximum magnetic field is equal to the applied field (); however, the interior field for iron becomes much smaller due to the large permeance.

As seen from the equations, the field distribution is quite analogous in all cases. The skin depth is the only parameter to define. The distribution curve may suggest a wave propagation into the interior. However, this phenomenon is not the electromagnetic wave defined by Maxwell's equations, but rather the result of diffusion of the magnetic field, which occurs at a variable speed.

Reference

[1] G. Lehner, Electromagnetic Field Theory for Engineers and Physicists (M. Horrer, trans.), New York: Springer, 2009.