Skin Effect - Examples

Examples

We can derive a practical formula for skin depth as follows:

where

the skin depth in metres

the relative permeability of the medium

the resistivity of the medium in Ω·m, also equal to the reciprocal of its conductivity: (for Copper, ρ = 1.68×10-8 Ω·m)

the frequency of the current in Hz

Gold is a good conductor with a resistivity of 2.44×10-8 Ω·m and is essentially nonmagnetic: 1, so its skin depth at a frequency of 50 Hz is given by

Lead, in contrast, is a relatively poor conductor (among metals) with a resistivity of 2.2×10-7 Ω·m, about 9 times that of gold. Its skin depth at 50 Hz is likewise found to be about 33 mm, or times that of gold.

Highly magnetic materials have a reduced skin depth owing to their large permeability as was pointed out above for the case of iron, despite its poorer conductivity. A practical consequence is seen by users of induction cookers, where some types of stainless steel cookware are unusable because they are not ferromagnetic.

At very high frequencies the skin depth for good conductors becomes tiny. For instance, the skin depths of some common metals at a frequency of 10 GHz (microwave region) are less than a micron:

Thus at microwave frequencies, most of the current flows in an extremely thin region near the surface. Ohmic losses of waveguides at microwave frequencies are therefore only dependent on the surface coating of the material. A layer of silver 3 μm thick evaporated on a piece of glass is thus an excellent conductor at such frequencies.

In copper, the skin depth can be seen to fall according to the square root of frequency:

In Engineering Electromagnetics, Hayt points out that in a power station a bus bar for alternating current at 60 Hz with a radius larger than one-third of an inch (8 mm) is a waste of copper, and in practice bus bars for heavy AC current are rarely more than half an inch (12 mm) thick except for mechanical reasons.