The Skin Effect in AC Circuits

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Discussion Overview

The discussion centers around the skin effect in AC circuits, exploring the physical mechanisms that cause charge carriers to be confined to a thin layer near the surface of conductors at higher frequencies. Participants seek explanations and references related to this phenomenon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that in DC circuits, charge carriers move uniformly through the entire cross-sectional area of the wire, while in AC circuits, the current is constrained to a "skin" near the surface, with the effect becoming more pronounced at higher frequencies.
  • Another participant explains that in a medium with finite conductivity, the current diffuses into the conductor from the outside, with the amplitude of the current decaying exponentially as one moves inward.
  • A different viewpoint discusses how AC currents generate azimuthal magnetic fields that induce eddy currents, which oppose the primary magnetic field and push the AC currents toward the outer edge of the conductor. This results in an effective AC resistance related to the skin depth.
  • A participant references a specific source, Smythe's "Static and Dynamic Electricity," for a detailed solution of the skin depth problem in cylindrical conductors.

Areas of Agreement / Disagreement

Participants appear to share an interest in understanding the skin effect, but there is no explicit consensus on the best explanation or source material. Multiple perspectives on the mechanisms involved are presented without resolution.

Contextual Notes

Some assumptions regarding the definitions of terms like "skin depth" and the conditions under which the skin effect occurs may not be fully articulated. The discussion does not resolve the complexities of the skin effect in different conductor geometries or materials.

Who May Find This Useful

This discussion may be useful for students and professionals interested in electrical engineering, physics, and materials science, particularly those exploring AC circuit behavior and electromagnetic theory.

atrevelyn314
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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!
 
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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.
 
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:
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!
 

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