This talk will review some recent developments that confirm the engineering prediction of H^T . ( M H^M) 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 was used as a transmitter and M is rank 2 polarization or polarizability tensor that describes the shape and material properties of the object. We will discuss how a recently derived asymptotic formula for the perturbed magnetic field due to the presence of a conducting object that involves a rank 4 tensor does in fact reduce to a formula involving a complex symmetric rank 2 tensor with at most 6 independent coefficients. For objects with rotational or reflectional symmetries the number of independent coefficients is still smaller. The talk will also show how the new tensors for different objects can be accurately computed by solving a vector valued transmission problem by hp-version finite elements. The ability to compute these tensors for different objects holds great promise for applications that involve the location and characterisation of conducting objects such as landmine detection, ensuring food safety and security screening.