Magnetic traction force in an HGMS with an ordered array of wires: I

The magnetic traction force, experienced by a paramagnetic sphere inside an infinite ordered array of wires that forms the matrix of an HGMS, is calculated. A comparison is made, for a particular case, with the forces (exact and approximate) due to a single wire and to two wires. It is found that the single wire forces are reasonably good approximations for high applied fields and small filling factors provided they are made to vanish midway between two adjacent wires.