Non-inverse-square force–distance law for long thin magnets

Abstract 

Objective

There is a need for a means of characterizing permanent magnets for dental applications, in particular the force–distance relationship. Problems with determining this on the basis of elementary theory prompted consideration of a model system of long thin magnets.

Materials and methods

(a) The force exerted by rod-shaped magnets (Alnico V, 3mm diameter, 170mm long) perpendicular to a large steel plate, as a function of distance, at small separations (<5mm), was determined for 85 examples. (b) Numerical modelling for a “polar disc” or sheaf of dipoles was conducted to test an alternative physical representation to the normally assumed simple dipole. (c) Exploratory curve-fitting trials were undertaken on the basis of known boundary conditions and observation of actual behaviour.

Results

The inverse square law for a point-like pole was found not to apply to the experimental data in any region. The polar disc model was found to provide a very good fit to the experimental data over the whole range tested, but only when an offset (∼1mm) of the pole position from the magnet face was assumed, and that this offset experienced an exponential-decay pole-position relaxation (typically 0.4–1.5mm). The fitted pole strength was of the order of 0.18mAm.

Significance

The implications of these results are that the commonly used elementary view of a simple dipole magnet is of little value for understanding the force–distance relationship and cannot be used as a basis for dental device characterization.

Keywords: Magnets, Force, Distance, Theory, Curve-fitting