LXI. The design of pole pieces of electromagnets and the forces acting on small bodies placed in their magnetic fields

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Abstract
Air gaps between electromagnet pole pieces of various shapes are considered from the point of view of the mechanical force on a small para- or diamagnetic body placed at any point in them. Assuming the face of a pole piece to be a magnetic equipotential surface, the theory of conformal transformations is applied to the two-dimensional figure formed by a transverse section of the pole pieces and air gap. Faces whose sections are given by the curves r8/2 cos 3θ/2 = constant are shown to produce a field such that the mechanical force on a small weakly magnetic body is constant in magnitude everywhere in the air gap. The direction of this force is along a radius vector drawn from the origin of co-ordinates to the point in question. Such a field is of use in susceptibility measurements with a torsion balance. Other cases considered are (a) a convex circular cylinder facing a plane pole piece, (b) a concave circular cylinder facing a plane pole piece. Some experimental tests of the theory are described. The force on a small weakly magnetic body placed near a short bar-magnet is calculated, and curves of motion of such a body, analogous to, but distinct from, lines of force are obtained.

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