The Skin Effect in AC Circuits

[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!

 

[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.

 

[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

 

[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!

 

[PJC01]

The skin effect in AC circuits is a result of electromagnetic induction. As the frequency of the AC current increases, the changing magnetic field around the wire induces an opposing electric field that pushes the charge carriers towards the surface of the wire. This effect is known as the "skin effect" because it causes the current to flow primarily on the outer surface of the wire, creating a thinner "skin" of current.

This phenomenon can be explained by the laws of electromagnetism, specifically Faraday's law of induction and Lenz's law. As the AC current changes direction, the magnetic field around the wire also changes, creating an opposing electric field that pushes the charge carriers towards the surface of the wire. This results in a higher concentration of charge carriers near the surface, leading to a higher current density and reducing the effective cross-sectional area of the wire.

To understand this concept in more detail, you can refer to textbooks or online resources on electromagnetism and AC circuits. Some possible sources include "Introduction to Electrodynamics" by David J. Griffiths and "Fundamentals of Electric Circuits" by Charles K. Alexander and Matthew N.O. Sadiku. These resources provide a mathematical explanation of the skin effect and its relationship to the frequency of the AC current.