The Thomson problem concerns the equilibrium positions of identical point charges constrained to move, without friction, on the surface of a sphere. Instead of motion constrained to a sphere, we consider motion in a central field with varying exponents, produced by a spherically symmetric charge density inside the sphere, with a total charge opposite to that of the point particles. For the case of a constant charge density in the sphere, the default setting, this is exactly the configuration that Thomson studied as a model for atoms (the plum pudding model), which suggested the present problem. The equilibrium positions are found here by the relaxation method—that is, by friction-damped motion from random stationary initial positions of the particles. Remarkably, the particles find their final resting positions on a spherical surface, although a naive expectation might favor a configuration with differing radial positions.