skin_depth

# Skin depth

 Stan Zurek, Skin depth, Encyclopedia-Magnetica.com, {accessed 2020-11-26}

## Definition

Skin depth (often denoted by lower-case Greek letter delta δ) - such a depth of penetration of alternating current or electromagnetic field, at which the amplitude is reduced to a value of 1/e (around 37%), as compared to the amplitude at the surface of the conductor.

Skin depth is a function of frequency of current, as well as magnetic permeability and electric resistivity (or conductivity) of the conductor in question.

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For good conductors (like most metals) the function can be defined as:1)

 $$\delta = \sqrt{\frac{2 · \rho }{\omega · \mu_r · \mu_0}} = \frac{1}{\sqrt{\pi · f · \mu_r · \mu_0 · \sigma}}$$ (m)

where: π - mathematical constant, f - frequency (Hz), μr - relative permeability of the conductor, μ0 - magnetic permeability of free space (H/m), σ - electric conductivity (S/m), ρ = 1 - electric resistivity (Ω·m), ω = 2·π·f - pulsation frequency (rad/s).

Skin depth vs. frequency for some materials (red line denotes 50 Hz):

by S. Zurek, Encyclopedia Magnetica, CC-BY-3.0