### Table of Contents

# 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), *μ _{r}* - relative permeability of the conductor,

*μ*- magnetic permeability of free space (H/m),

_{0}*σ*- electric conductivity (S/m),

*ρ*= 1

*/σ*- electric resistivity (Ω·m),

*ω*= 2·

*π·f*- pulsation frequency (rad/s).

- light grey (
**Al**) - metallic aluminium - orange (
**Cu**) - metallic copper - green (
**steel 410**) - magnetic stainless steel, grade 410 - blue (
**Fe-Si**) - grain-oriented electrical steel - dark grey (
**Fe-Ni**) - permalloy (80%Ni-20%Fe)

^{S. Zurek, E-Magnetica.pl, CC-BY-4.0}

## Calculator of skin depth

The calculator uses the following equation: $$ \delta = \sqrt{\frac{\rho }{\pi · f · \mu_r · \mu_0}} $$ | |

→ → → Helpful page? Support us!→ → → | PayPal | ← ← ← Help us with just $0.10 per month? Come on… ← ← ← |