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🔌 Skin Effect

Interactive skin effect simulation: visualise how AC current concentrates near the surface of a conductor. Adjust frequency and material to see skin depth δ change in real time.

Electromagnetism3DEasy60 FPS

About this simulation

This simulator renders a real cross-section heatmap of J(d) = J₀e^(−d/δ), where δ = √(ρ/πfμ) is computed live from the resistivity ρ and relative permeability μᵣ of the chosen material — Copper, Aluminium, Iron, or Stainless Steel. As you raise the Frequency slider, δ shrinks and the yellow-white high-current shell visibly thins toward the conductor's surface, while the side panel plots the exact exponential decay curve against depth in units of δ.

🔬 What it shows

Why alternating current does not spread evenly through a wire's cross-section: eddy currents induced by the AC magnetic field oppose current in the interior, crowding it into a thin surface shell whose thickness is the skin depth δ.

🎮 How to use

Pick a Material from the dropdown, drag Frequency f (log scale, 50 Hz to 10 MHz) and Conductor radius to watch the heatmap and δ boundary ring update, and read live R_AC/R_DC and r/δ ratios in the Stats panel; Pause (P) freezes the AC pulse animation and Reset (R) restores defaults.

💡 Did you know?

Iron's high permeability (μᵣ ≈ 200) gives it a tiny skin depth even at ordinary 50/60 Hz power-line frequencies — which is exactly why transformer cores must be built from thin laminated sheets instead of solid iron blocks, to break up eddy-current loops.

Frequently asked questions

What is skin depth δ?

Skin depth is the distance below a conductor's surface at which AC current density has fallen to 1/e (about 37%) of its surface value; it is given by δ = √(ρ/πfμ), so it shrinks as frequency f or permeability μ increases.

Why does current avoid the centre of the wire at high frequency?

The changing magnetic field inside the conductor induces eddy currents that oppose the original current in the interior and reinforce it near the surface, so at high frequency almost all the current is confined to a thin outer shell of thickness ~δ.

How does R_AC/R_DC relate to skin depth?

When the conductor radius r is much larger than δ, effectively only a thin annulus of thickness δ carries current, so the AC resistance rises roughly as R_AC/R_DC ≈ r/(2δ) compared to the DC case where the whole cross-section conducts.

Why do RF engineers use Litz wire or hollow conductors?

Since current at high frequency only flows in a thin surface shell anyway, the solid core of a wire carries little current, so Litz wire (many thin, individually insulated strands) or hollow tubing reduces AC resistance and material cost without giving up conductivity.

Why are transformer cores laminated?

Iron's high permeability makes its skin depth very small even at 50/60 Hz, so eddy currents would otherwise circulate through a solid iron core and waste energy as heat; thin insulated laminations break these loops and cut eddy-current losses.

⚙ Under the hood

See how AC current concentrates near the surface of a conductor. Interactive heatmap shows current density J = J0 e^(-d/delta) with the skin depth updated live.

Canvas 2DElectromagnetismSkin EffectACConductor

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install