The control of the strength and pattern of magnetospheric convection by the interplanetary magnetic field (IMF) is well established. This control is widely interpreted as evidence for magnetic interconnection between the IMF and the magnetosphere. A quantitative model of a magnetically interconnected ("open") magnetosphere is developed in this thesis. The model is based on the perturbation of a closed magnetic field configuration with a given magnetopause geometry. The internal field is the result of a dipole field confined by Chapman-Ferraro currents at the magnetopause and stretched on the nightside to produce a tail field. The external field is taken from a model based on gas-dynamic supersonic flow around a blunt object with an embedded magnetic field. The normal component at the magnetopause must be time independent and it is derived from two different hypotheses of magnetopause merging. The interconnection field is derived as a solution to a Neumann boundary value problem consisting of Laplace's equation with the magnetopause normal component distribution as a boundary condition. This interconnection field is then added to the closed models to produce the desired open configuration. The resulting open magnetospheric configuration is used to map magnetopause electric fields down to the ionosphere in the polar cap thus producing electrostatic potential contours. Various distributions result as a function of the IMF orientation and of merging hypothesis. The results can be compared with existing data to test and refine the model.