Penetration depth / skineffect

It is a known phenomenon, when an alternating current passes through a conductor, current distortion or displacement occurs, a phenomenon whereby the current density in the conductor decreases with increasing depth.

This current displacement towards the surface of the conductor increases with increasing frequency. So, for example, in a copper rod of 1 cm thickness in which an H.F. current with a frequency of 1 MHz flows,  practically all the current is concentrated in a surface layer with a thickness of only 0.1 mm. This phenomenon is called the skin effect. With the aid of Maxwell’s equations it can be shown that the current density decreases exponentially with depth. At a frequency of 50 Hz is the (effective) depth of penetration from about 1 cm, at 10 kHz is the (effective) depth of penetration already less than 1 mm and at 10 Mhz is the (effective) penetration depth only 20µm (steel), which means that in this last frequency power actually only runs on the surface. The consequence of the skin effect is that the resistance of a conductor increases significantly at higher frequencies.

Formula for calculating the depth of penetration:

In this formula: f (in Hertz )is the frequency of the magnetic field, µ_r in Henry/meter is the permeability of the material, σ in Siemens/meter is the specific conductivity of the material. δ the penetration depth in meters.