Janhavi S Agashe and David P Arnold 2008 J. Phys. D: Appl. Phys. 41 105001 doi:10.1088/0022-3727/41/10/105001
Janhavi S Agashe and David P Arnold
Show affiliationsKelvin's formula is used to calculate forces acting on a permanent magnet in the presence of an external magnetic field from a second permanent magnet. This approach is used to derive explicit analytical solutions for the axial and lateral forces between cuboidal and cylindrical permanent magnets as functions of magnet dimensions and separation. While exact solutions can be found for cuboidal magnets, a hypergeometric expansion is used to approximate the elliptic integrals in solving for the fields and forces for the cylindrical magnets. The resulting equations are applied over a range of magnet sizes and geometries to explore scaling laws and other geometrical effects. It is shown that cuboidal magnets provide larger forces than equivalently sized cylindrical magnets. Also, the aspect ratio of the magnets significantly affects the forces. These results are intended to benefit the design and optimization of sensors, actuators and systems that rely on magnetic forces, particularly at the microscale.
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
Issue 10 (21 May 2008)
Received 17 January 2008, in final form 29 February 2008
Published 9 April 2008
A Corrigendum for this article has been published in 2009 J. Phys. D: Appl. Phys. 42 099801
Janhavi S Agashe and David P Arnold 2008 J. Phys. D: Appl. Phys. 41 105001