Understanding the magnetic polarizability tensor

Ledger, Paul D.; Lionheart, W. R. Bill

Abstract

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects.

Citation

Ledger, P. D., & Lionheart, W. R. B. (2016). Understanding the magnetic polarizability tensor. IEEE Transactions on Magnetics, 52(5), 1-16. https://doi.org/10.1109/tmag.2015.2507169

• Journal Article Type: Article
• Acceptance Date: Dec 9, 2015
• Online Publication Date: Dec 9, 2015
• Publication Date: 2016-05
• Deposit Date: Jun 12, 2023
• Journal: IEEE Transactions on Magnetics
• Print ISSN: 0018-9464
• Electronic ISSN: 1941-0069
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 5
• Pages: 1-16
• DOI: https://doi.org/10.1109/tmag.2015.2507169
• Keywords: Electrical and Electronic Engineering; Electronic, Optical and Magnetic Materials