Skindra

Meet Skindra, an alternating current that crowds toward the surface of her wire.

A changing current makes a changing magnetic field inside the wire, and that field induces eddy currents that oppose current in the centre and reinforce it near the surface. The result is that AC current density falls off with depth below the surface. The skin depth δ = √(2ρ/(ωμ)) is the depth at which it has fallen to about 37 percent, 1/e, of its surface value.

For copper at 60 hertz, with ρ = 1.68×10⁻⁸ ohm-metres, δ is about 8.4 millimetres. At radio frequencies it shrinks dramatically, because δ goes as one over the square root of frequency.

Because of the skin effect, high-frequency circuits use hollow tubes, silver-plated conductors or braided 'Litz' wire, and induction heating concentrates heat near a metal's surface.

The formula is the good-conductor approximation. It assumes a uniform conductor much thicker than δ, and it loses accuracy for very high frequencies or poor conductors.