Optimization of on-axis magnetic field of uniformly magnetized cones

Abstract

The magnetic field B induced along the axis of symmetry of axially magnetized cones was studied analytically and experimentally for various cone angles α. An explicit algebraic equation was derived for sharp-pointed and truncated cones. A sharp cone is characterized by singularities of B and ∇B at its apex point. For a truncated cone, the maximum values of these quantities are achieved for αmax∼54.7° and α∇∼39.2°, respectively. Two truncated cones with αuni∼63.4° positioned in a mirrored co-apex configuration produce a uniform axial field in the free-space gap. For smaller angles, the minimum field is located in the center of the airgap, while for larger, it is at the cones’ surfaces with extremum at αmin∼71.6°. These predictions were investigated using a tunable apparatus in which Co–Fe cones are magnetized by cylindrical NdFeB magnets. Strong ∼4 T B-field was achieved. Experimental results are discussed in detail, including incomplete magnetization and other secondary effects.