⚡ Skin Effect — AC Current in Conductors
When alternating current flows through a conductor, eddy currents push the current density towards the surface. The current density decays exponentially: J(d) = J₀ e−d/δ where δ = √(ρ/πfμ) is the skin depth. At high frequencies, most current flows in a thin shell — increasing resistance dramatically.
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Skin Depth Formula
The skin depth is δ = √(ρ / π f μ) where ρ is electrical resistivity (Ω·m), f is frequency (Hz) and μ = μrμ₀ is the magnetic permeability. For copper at 50 Hz, δ ≈ 9.4 mm; at 1 MHz it shrinks to just 66 μm.
The AC resistance of a round conductor of radius r is approximately RAC/RDC ≈ r / (2δ) when r ≫ δ. For r ≈ δ the ratio approaches 1 (nearly DC behaviour).
Why It Matters
At radio frequencies the skin effect confines current to a thin shell, so engineers use hollow conductors (the core carries no current anyway) or Litz wire — many thin, individually insulated strands woven together so each strand sees a smaller skin effect. Transformer cores are laminated to break eddy current loops (the same phenomenon in ferromagnetic materials).
Applications
RF transmission lines, microwave waveguides, high-frequency PCB traces, induction heating (deliberately using skin effect to heat only the surface), MRI coils, and shielding design all require accounting for the skin effect. Iron has high permeability μr ≈ 200 which makes its skin depth very small even at power-line frequencies — that is why transformer cores must be laminated even at 50/60 Hz.