IEEE Transactions on Magnetics

The purpose of this paper is to clear up a major mystery in metal detection and confirm that the engineering prediction of H T ¨pM ind H M q, for the sensitivity of measurements of the perturbed magnetic field to the presence of a general conducting object placed in a low frequency background field, is correct.Explicitly, H T is the background field generated by the transmitter coil, H M is the background field generated by the receiving coil as if it were used as a transmitter and M ind is a rank 2 polarisation tensor, which describes the shape and material properties of the object.To show this, we apply a recently derived asymptotic formula for the perturbed magnetic field due to the presence of a conducting object, which is expressed in terms of a new class of rank 4 polarisation tensors (H.