Abstract

Objective: Miniature magnets are used in dentistry, principally for the retention of prosthetic devices. The relationship between force and separation of a magnet and its keeper, or, equivalently, two such magnets, has been neither defined theoretically nor described practically in any detail suitable for these applications. The present paper addresses this lacuna.

Methods: A magnet is considered as a conglomeration of magnetic poles distributed over a surface or a solid in three-dimensional space, with the interaction of poles governed by the Coulomb law. This leads to a suite of mathematical models. These models are analysed for their description of the relationship between the force and the separation of two magnets.

Results: It is shown that at a large distance of separation, an inverse power law must apply. The power is necessarily integer and at least two. All possibilities are exhausted. Complementarily, under reasonable assumptions, it is shown that at a small distance of separation, the force remains finite.

Significance: The outcome is in accordance with practical experience, and at odds with the use of simple conceptual models. Consequences relevant to the usage of magnets in dentistry are discussed.

Keywords: Coulomb law; Force–distance relationship; Fourier cosine transform; Limiting behaviour; Magnets; Power series expansion.