Optimization of on-axis magnetic field of uniformly magnetized cones

The magnetic field B induced along the axis of symmetry of axially magnetized cones was studied analytically and experimentally for various cone angles a. An explicit algebraic equation was derived for sharp-pointed and truncated cones. A sharp cone is characterized by singularities of B and del B at its apex point. For a truncated cone, the maximum values of these quantities are achieved for alpha(max) similar to 54:7 degrees and alpha(del) similar to 39:2 degrees, respectively. Two truncated cones with alpha(uni) similar to 63:4 degrees 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 alpha(min) similar to 71:6 degrees. These predictions were investigated using a tunable apparatus in which Co-Fe cones are magnetized by cylindrical NdFeB magnets. Strong similar to 4 T B-field was achieved. Experimental results are discussed in detail, including incomplete magnetization and other secondary effects.