20 May Back to Basics — Skin Depth

If you’ve ever studied electricity, you know that alternating current (AC) tends to distribute itself inside a conductor in such a way that the current density is highest near the surface of the conductor. This is called the skin effect. This effect is caused by the eddy currents induced in the material that oppose the changing magnetic field produced by the coil.

How deep eddy currents penetrate into a material is defined as the depth at which their intensity drops to 1/e (about 37 %) of their original intensity. This is the standard, theoretical depth. It’s a function of the inducing coil’s current frequency, as well as the electrical conductivity and the magnetic permeability of the material.

So, the skin effect impacts penetration depth and the ability of eddy currents to detect defects.

High or Low?

Penetration depth (more commonly known as skin depth) is greater at low frequency, conductivity, and permeability. Skin depth decreases as these values increase. Since you don’t have any control over conductivity or permeability, frequency is your best ally. Thus, depending on the type of defect you’re looking for, but more importantly where these defects are located in the material, you want to choose a frequency that will give you an adequate eddy current penetration. The rule of thumb is for defects to be within one to two skin depths from the surface to get good far-side indication detection.

Depth-to-Frequency Graph

Calculating Skin Depth

So, theoretically, for eddy current, skin depth would be:

δ ≈ 1/√πfμσ


Permeability and conductivity are readily available for all materials on the market where such a properties are a concern.

Real-World Considerations

There is a big gap between theory and reality, though.

Materials to be tested can be non-ferromagnetic or ferromagnetic. According to what I’ve said before, eddy currents don’t usually do very well on ferromagnetic materials because the permeability of such materials is typically too high to get good penetration unless operating at very low frequencies. However, such frequencies require coils with more windings, ergo larger coils, which lowers probe resolution and makes results noisier. So, while eddy current testing (ECT) is possible in ferromagnetic materials, it’s a bit touch and go.

Historically, there have been technical limitations to low-frequency ECT because commercially available test instruments simply could not supply the necessary low frequencies. Nowadays, most available test instruments deliver frequencies as low as 5 Hz to several tens of megahertz.

Permeability is, also, not uniform. It varies within the material. So even if the proper penetration can be achieved in ferrous materials, most of the time the level of noise is higher than in non-ferromagnetic materials. This is why other electromagnetic technique have been developed.

There are also other factors that enter into play as explained in Florian Hardy’s excellent article On the Sensitivity of Transmit-Receive Probes. In a nutshell, sensitivity is affected by thermal drift at low frequencies and resonance with the probe’s cable at high frequencies. These also have to be taken into consideration when choosing an operating frequency for inspection. It should be said, however, that modern probe design take these aspects into consideration, so they are not immediate concerns in most inspection scenarios.


Results using electromagnetic inspection methods like ECT and eddy current array (ECA) are only as good as how you set up your inspection, and this setup depends on your intimate knowledge of three things:

  • Coil frequency
  • Magnetic permeability of the material under test
  • Electrical conductivity of the material under test

As two of these properties are intrinsic to the material under test, the importance of knowing exactly what material you’re testing cannot be stressed enough. The more intimate your knowledge of the material under test, the better you can choose an operating frequency, and the better your inspection results will turn out to be.

Check out our lines of surface and tubing probes to find the one that suits your needs.


Basics Electromagnetic testing NDT Technology

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