Table of Contents
Magnetic and Electrical Separation
Volume 9 (1998), Issue 1, Pages 39-52

An Analytic Solution for the Force Between Two Magnetic Dipoles

Hughes Space and Communications Company, P.O. Box 92919, Los Angeles 90009, CA, USA

Received 7 February 1997; Accepted 30 April 1998

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An analytic equation describing the force between two magnetic dipoles is derived in this paper. We assumed that the dipole sizes are small compared to their separation. A Taylor expansion for the first non-zero term was performed in order to derive the magnetic force analytic expression. Vector differential and path integral derivation approaches are used, and the same result is achieved with both methods. This force decreases with the fourth power of the distance between the dipoles. Accuracy estimates due to the Taylor approximation are given.