SkinDepthFormel

SkinDepthFormel, commonly referred to as the skin depth, is a length scale that describes how far alternating magnetic fields and the associated current penetrate into a conducting material. When a conductor carries an AC current at angular frequency ω, the induced current density and the magnetic field decay with depth, concentrating near the surface. The characteristic depth δ is defined by the skin depth formula.

The skin depth δ is given by δ = sqrt(2/(ω μ σ)), where ω = 2π f is the angular frequency, μ is the magnetic permeability of the material (μ = μ0 μr, with μ0 ≈ 4π×10^-7 H/m), and σ is the electrical conductivity in siemens per meter. For non-magnetic materials, μr is approximately 1, so μ ≈ μ0; in ferromagnetic materials, μr can be much larger, reducing δ accordingly.

This relationship arises from solving Maxwell’s equations for a good conductor, yielding an exponential attenuation of current with depth: J(z) ≈ J0 e^{-z/δ} and a corresponding decay of the magnetic field B(z). Consequently, at higher frequencies the effective cross-section for current is reduced, increasing the AC resistance due to the skin effect. Conversely, lower frequencies or materials with higher conductivity yield larger skin depths.

Typical values illustrate the scale: copper at 60 Hz has a skin depth around 8–9 mm, while at radio frequencies δ becomes much smaller. Applications of the SkinDepthFormel include RF wiring and components, electromagnetic shielding, induction heating, and the analysis of high-frequency current distribution. Limitations arise from assumptions of homogeneity, simple geometry, and constant material properties; frequency-dependent μ and σ, anisotropy, and surface roughness can modify actual skin depths.