Analysis of torque in nested magnetic cylinders

Abstract

Rotatable nested cylindrical magnets may be used to generate variable magnetic fields. A mutual torque exists between the cylinders which is an important consideration in practical designs. We present a thorough investigation of this torque, combining experiment, computation, and theory. In the finite length case, in which the magnetization varies according to the prescription of Halbach, the torque is an end effect. It is proportional to sin α, where α is the angle defining the relative orientation of the cylinders. Practical designs use a discrete number N of permanent magnet segments to approximate the continuously varying magnetization of the ideal design. These introduce higher components sin(nα) to the angular dependence of torque, where the allowed values of n are restricted to n=(kN±1) according to the segmented magnet torque theorem.