skin_depth

# Skin depth

 Stan Zurek, Skin depth, Encyclopedia Magnetica, http://www.e-magnetica.pl/doku.php/skin_depth

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.

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):

## Calculator of skin depth

 The calculator uses the following equation: $$\delta = \sqrt{\frac{\rho }{\pi · f · \mu_r · \mu_0}}$$ frequency f = (Hz) (kHz) (MHz) (GHz)       resistivity ρ = (μΩ·cm) (μΩ·m) (Ω·cm) (Ω·m) relative permeability μr =             skin depth δ = (nm) (μm) (mm)
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