⚡ Skin Effect — AC Current in Conductors

When alternating current flows through a conductor, eddy currents push the current density towards the surface. The current density decays exponentially: J(d) = J₀ e^−d/δ where δ = √(ρ/πfμ) is the skin depth. At high frequencies, most current flows in a thin shell — increasing resistance dramatically.

Skin depth δ—

r/δ ratio—

R_AC/R_DC—

Material

Parameters

Frequency f 50 Hz Conductor radius 10 mm

Stats

Skin depth δ—

r/δ—

R_AC/R_DC—

Frequency f—

MaterialCopper

Keyboard

P Pause / Play
R Reset

Skin Depth Formula

The skin depth is δ = √(ρ / π f μ) where ρ is electrical resistivity (Ω·m), f is frequency (Hz) and μ = μ_rμ₀ is the magnetic permeability. For copper at 50 Hz, δ ≈ 9.4 mm; at 1 MHz it shrinks to just 66 μm.

The AC resistance of a round conductor of radius r is approximately R_AC/R_DC ≈ r / (2δ) when r ≫ δ. For r ≈ δ the ratio approaches 1 (nearly DC behaviour).

Why It Matters

At radio frequencies the skin effect confines current to a thin shell, so engineers use hollow conductors (the core carries no current anyway) or Litz wire — many thin, individually insulated strands woven together so each strand sees a smaller skin effect. Transformer cores are laminated to break eddy current loops (the same phenomenon in ferromagnetic materials).

Applications

RF transmission lines, microwave waveguides, high-frequency PCB traces, induction heating (deliberately using skin effect to heat only the surface), MRI coils, and shielding design all require accounting for the skin effect. Iron has high permeability μ_r ≈ 200 which makes its skin depth very small even at power-line frequencies — that is why transformer cores must be laminated even at 50/60 Hz.

About this simulation

Last updated: 5 July 2026

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.