Abstract: A permanent magnet having a shell of magnetic material and a hollow cavity. The shell is permanently magnetized to produce an axially tapered magnetic field in the cavity. In one embodiment, a segmented spherical magnetic shell has a concentric spherical cavity. An access port in the form of an axial hole passes through polar segments of the shell along its polar axis P. The shell ("magic sphere") is magnetized such that it is capable of producing a tapered magnetic field in the cavity. Both the magnitude and direction of the remanence B.sub.R of the shell material vary from segment to segment. Another embodiment shows a segmented cylindrical shell in the form of a ("magic ring"). The shell material has a magnetic remanence B.sub.R that varies in magnitude and direction from segment to segment. The shell produces a axially tapered field in the cavity.