title: 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.
  
  
  METHODS
  (a) The force exerted by rod-shaped magnets (Alnico V, 3mm diameter, 170 mm 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 ( approximately 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 0.18 mAm.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Dental Materials Science, Faculty of Dentistry, Prince Philip Dental Hospital, The University of Hong Kong, 34 Hospital Road, Hong Kong. b.w.darvell@hku.hk
authors.forename: B W
authors.initials: BW
authors.lastname: Darvell
authors.forename: A P L H
authors.initials: AP
authors.lastname: Dias
mesh_terms: D003799:Dental Stress Analysis; D003781:Denture Retention; D006112:Gravitation; D008280:Magnetics / Q000295:instrumentation*; D009967:Orthodontic Appliances