# Generalised Magnetic Polarizability Tensors

## TL;DR

This paper develops a new asymptotic expansion for magnetic field perturbations caused by small conducting objects, enabling better shape and material identification crucial for applications like metal detection and security screening.

## Contribution

It introduces a novel class of generalized magnetic polarizability tensors with explicit formulas, advancing the characterization of small objects in electromagnetic fields.

## Key findings

- Provides explicit formulas for polarizability tensors.
- Enhances shape and material property discrimination.
- Improves small object detection in practical applications.

## Abstract

We present a new complete asymptotic expansion for the low frequency time-harmonic magnetic field perturbation caused by the presence of a conducting (permeable) object as its size tends to zero for the eddy current regime of Maxwell's equations. The new asymptotic expansion allows the characterisation of the shape and material properties of such objects by a new class of generalised magnetic polarizability tensors and we provide an explicit formula for their calculation. Our result will have important implications for metal detectors since it will improve small object discrimination and, for situations where the background field varies over the inclusion, this information will be useable, and indeed useful, in identifying their shape and material properties. Thus, improving the ability of metal detectors to locate landmines and unexploded ordnance, sort metals in recycling processes, ensure food safety as well as enhancing security screening at airports and public events.