Penetration and skin depth in 'metallic' magnetic induction tomography (classical electromagnetism)

Question

Does anyone know how AC magnetic fields behave in 'metallic' magnetic induction tomography (MIT). Do they form a magnetic circuit around a metallic specimen or penetrate through it, or both? This would be in respect of the skin effect limiting the penetration of the AC magnetic driving field (primary).

MIT works by an AC magnetic driving field inducing eddy currents in a metallic specimen (to be imaged) and sensors (coils) on the other side of the specimen picking up the secondary magnetic field due to the eddy currents induced in it. It actually senses or picks up the total field (secondary and primary magnetic fields). Sensor coils measure the spatially distributed total fields to be tomographically represented as an image.

Answer 1

The answer is both. The magnetic fields form a magnetic circuit around the metallic sample and they also penetrate the sample to be detected on the other side by sensor coils. This answer was obtained by asking experts in the field of MIT (magnetic induction tomography). I think it would be difficult to find in a text book.

I will attempt a fuller answer as follows. There are reluctance paths (magnetic resistance) of the magnetic field through air around the metallic sample, but also a reluctance path around the surface of the sample (see diagram). This in the DC case. In the AC case, the magnetic field penetrates the sample w.r.t. the skin effect. But the magnetic circuit around the sample is more complicated than the DC case, as back e.m.f.'s produce flux distortions in the material of the sample and changes in the material cause more flux distortions.