The response of an ideally soft magnetic cylinder is calculated by approximating magnetostatic interactions while taking into account the exchange energy of curling patterns with point singularities. Detailed calculations of the magnetic surface charge distribution of paramagnetic materials are used as a guide in parameterizing an approximate charge distribution suitable for applying the Ritz method to the micromagnetic problem of ferromagnetic materials without anisotropy or magnetostriction. Numerical results are given for a cylinder with L/D=1 for fields below saturation illustrating how remanence and coercivity depend on the ratio of the exchange length A/M2o to sample dimensions. The role of point singularities in remanence, coercivity, nucleation and irreversibility is outlined.