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.
