Eddy currents induced by a coil do not flow uniformly through the thickness of a conductor. The induced currents generate their own field opposing the driving field, so current density falls exponentially with depth. The standard depth of penetration delta is the depth at which eddy current density has fallen to 1/e, about 37 %, of its surface value, and follows directly from the skin-effect solution for a conducting half space: delta = 1 / sqrt(pi f mu sigma).

Everything in eddy current testing scales with this one number. Quartering the frequency doubles the depth; a material four times more resistive gives twice the depth; a relative permeability of 100 divides the depth by ten. That last term is why carbon and low alloy steels cannot be interrogated volumetrically with conventional eddy currents at useful frequencies, and why ferrous tubing is inspected with remote field or magnetically saturated probes instead.

The standard depth is not a detection limit. Flaws are routinely found at two or three standard depths, where the field is only 13 % or 5 % of the surface value, provided gain and signal-to-noise allow it. What actually caps the useful depth is phase: the current lags 57.3 degrees per standard depth, so at about three standard depths the flaw response has rotated close to 180 degrees, falls back on top of the lift-off direction, and can no longer be separated from it.

Use this to pick a starting frequency, to judge whether a far-surface or second-layer flaw is reachable at all, and to sanity check a procedure that specifies a frequency without saying why. For ferromagnetic material treat relative permeability as a variable, not a constant: it depends on the applied field, on stress, and on cold work.

Worked example

Material property entered as	rho
Electrical resistivity	72 uohm.cm
Conductivity	2.39 %IACS
Relative permeability	1
Test frequency	100 kHz
Wall or part thickness	1.5 mm
Standard depth of penetration	1.35 mm
Three standard depths	4.05 mm
Thickness in standard depths	1.11 x
Field strength at far surface	32.9 %
Conductivity	1.39 MS/m
Conductivity	2.39 %IACS

304 stainless (rho = 72 uohm.cm, mur = 1) at 100 kHz. In SI: rho = 7.2e-7 ohm.m, mu = 4pi x 1e-7 H/m, f = 1e5 Hz. pi.f.mu.mur = 3.14159 x 1e5 x 1.256637e-6 = 0.394784. rho / 0.394784 = 1.823781e-6, square root = 1.350475e-3 m = 1.350 mm. Cross-check with the 50-root rule: 50 x sqrt(72/100000) = 1.342 mm, 0.7 % low because the rounded constant 50 is used instead of the exact 50.33. Three standard depths = 4.05 mm. The 1.5 mm far surface sits at 1.5/1.350475 = 1.111 standard depths, where the field is 100 x e^-1.111 = 32.9 % of the surface value. Conductivity = 100/72 = 1.39 MS/m = 172.41/72 = 2.39 %IACS.

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