Force-Distance Relation for Dental Magnets – Fitted Equation

Objective: The force-distance power law for dental magnets had been unresolved until a theoretical study found that only even inverse powers were allowed; for simple magnets inverse fourth power was the only possibility. It remained to demonstrate that this indeed did apply to real magnets, the present purpose.

Methods: The force exerted by a series of real dental magnets to a large steel plate, and in a few cases to dental magnet keepers, as a function of distance was recorded. Curve-fitting of that data was explored. using the equation previously used for long dipoles, but allowing the power to be a free parameter. An index of 4 was the only feasible value. Corresponding fitted parameter values were then examined in relation to magnet design and each other.

Results: The theoretical power law index was confirmed to be 4. For a satisfactory fit, a ‘polar offset’ and a ‘stretch power’ were again required to better approximate the experimental results. Polar offset appears to be a function of apparent pole strength; stretch power less clearly so.

Significance: The motivating question is settled.