Skin Effect
3 min read
Alternating current does not use a conductor evenly. The changing magnetic field inside the metal opposes current hardest along the axis and pushes it toward the surface, and the effect strengthens with frequency. Less of the cross-section carries current, so the effective resistance rises above the DC value.
The mechanism is induction working against itself. Current in a wire sets up a magnetic field, an alternating current sets up a changing one, and a changing field inside the metal induces eddy currents that oppose the flow most strongly at the centre, where the enclosed flux is greatest. What is left is a current concentrated in a surface layer, and that layer thins as the square root of frequency.
The consequences are practical rather than exotic. In copper at mains frequency the layer runs to about nine millimetres, so ordinary wiring never notices. At a megahertz it is about sixty-five micrometres, and a solid conductor is then mostly dead weight carrying nothing. That is why litz wire exists, its many thin strands separately insulated and woven so each takes its turn at the surface; why RF conductors are silver plated, the surface carrying nearly all the current; and why heavy feeders are sometimes tubing rather than rod.
It also means a resistance read off a meter is the wrong figure for AC work. Resistivity and geometry give the DC value, and the AC value climbs above it as frequency rises. A neighbouring conductor makes matters worse, crowding the current further to one side. That is a separate mechanism called proximity effect, and it is why a tightly wound coil or a bundled cable loses more than a lone wire of the same size.
To put a number on it for a real wire, the skin depth calculator takes the frequency, the metal and the wire size and works out both the depth and the AC resistance. A copper wire 1 mm across is a fair example: at 100 kHz the skin depth is about a fifth of a millimetre, and the wire carries AC at roughly one and a half times its DC resistance.
Frequently asked questions
What is skin depth?
It is the depth below the surface where the current density has fallen to about 37% (1/e) of its value at the surface. For a good conductor it is δ = √(ρ / (π f μ)), so it shrinks with the square root of frequency: four times the frequency halves the depth.
What is the skin depth of copper at 50 Hz and at 1 MHz?
About 9.2 mm at 50 Hz, 8.4 mm at 60 Hz and 65 µm at 1 MHz, taking copper's resistivity as 1.68 × 10⁻⁸ Ω·m.
Does skin effect matter in house wiring?
Hardly. Ordinary wiring conductors are far thinner than the 9 mm skin depth at mains frequency, so the current uses nearly the whole cross-section. It starts to matter for very thick cables and busbars at mains frequency, and for almost any conductor at radio frequencies.
What is the difference between skin effect and proximity effect?
Skin effect is a wire's own changing field pushing its current to the surface. Proximity effect is the field of a nearby conductor pushing the current to one side. Both raise AC resistance, and they add up in tightly wound coils and bundled cables.