Skin Depth

Plate 20 speaks for itself: “At high frequency, current lives on the surface.”

The Physics

An alternating current induces eddy currents that push it toward the conductor's surface. It falls off with depth over a skin depth that shrinks as frequency rises.

δ = √(2ρ / (ω μ))

• δ: skin depth, m
• ρ: resistivity (Cu: 1.68×10⁻⁸ Ω m), Ω m
• ω: angular frequency 2πf, rad s⁻¹
• μ: permeability (Cu ≈ μ₀), H m⁻¹

AC current crowds into the outer skin. Copper at 60 Hz: δ ≈ 8.4 mm; at 1 MHz: 65 µm.

Sources

• CRC Handbook of Chemistry and Physics: Cu resistivity at 20 °C.
• J. D. Jackson, Classical Electrodynamics, 3rd ed., §8.1.

On the poster

Plate 020, “Skin Depth”: the pixel-art plate with its slogan “At high frequency, current lives on the surface.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.