# The Skin Effect in AC Circuits

1. Jun 15, 2010

### atrevelyn314

In DC circuits the charge carriers move uniformly through the entire cross sectional area of the wire. In AC circuits the current is constrained to travel in a thin "skin" just below the surface of the wire, effectively reducing the cross-sectional area of the wire. The effect becomes more pronounced the higher the frequency of the AC circuit.

Can anyone please give me a physical explanation of why the charge carriers are confined to the "skin" in an AC circuit. Or could you please direct me to a source where this is worked out explicitly?

Thank you!

2. Jun 15, 2010

### Antiphon

In a medium with finite conductivity the current slowly diffuses into the interior of the conductor from outside in. For a sinusoidal current the amplitude decays exponentially as you move into the conductor.

3. Jun 16, 2010

### Bob S

In a finite conductor, the ac currents generate azimuthal magnetic fields, which in turn generate eddy currents in the conductor. The eddy currents act to oppose the primary magnetic field, and force the ac currents to the outer edge of the conductor. the effective ac resistance of a cylindrical conductor is the equivalent to the resistivity of a conductor of area δ (the skin depth) times 2πR (the circumference).

The steady-state skin depth problem is solved exactly for cylindrical conductors in Smythe Static and Dynamic Electricity third edition, Section 10.02[STRIKE] using modified Bessel functions[/STRIKE].

Bob S

Last edited: Jun 16, 2010
4. Jun 16, 2010

### atrevelyn314

Thanks Bob S. That was very helpful. It surprises me that for such an interesting and seemingly common effect more textbooks don't discuss it. Jackson only talks about skin depth, but not the skin effect. Thanks again!