Calculator

Current Density Profile

Visualize how eddy currents distribute across a workpiece cross-section. Adjust frequency to see the transition from through-heating to surface-heating in real time.

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Current Density Visualizer

Skin Depth

δ = √( ρ / π · f · μ₀ · μᵣ )

Geometry

Material

Diameter

Frequency 10 kHz

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

Resistivity (ρ): — Rel. Permeability (μ_r): —

Cross-Section — Current Density Map

Low |J| High |J|

J₀

|J| / |J_surface| vs Depth from Surface

Skin Depth (δ)

—

d / δ Ratio

—

Power in 1st δ

—

Power in 2δ

—

Heating Regime

—

Frequency

—

Physics Behind the Visualization

Flat Slab

Current density decays exponentially from the surface into the workpiece. At one skin depth, current has fallen to 37% of its surface value.

J(x) / J₀ = e^−x/δ

Solid Cylinder

The cylindrical geometry focuses current differently. The exact solution uses modified Bessel functions (Kelvin functions ber and bei) to account for the converging geometry.

|J(r)| / |J(R)| = |I₀(kr)| / |I₀(kR)|