The early version of the Toffoletto - Hill - Ding open magnetosphere model is improved and generalized in this thesis. This model computes the interplanetary magnetic field (IMF) dependent magnetic and electric fields in the Earth's magnetosphere. The magnetospheric magnetic fields contain contributions from the Earth's dipole field, the ring current, the tail field, and the interconnection magnetic field that represents the effect of an open magnetosphere. The solar wind electric field is mapped along open magnetic field lines into the polar cap ionosphere and acts as a driver for magnetospheric convection. We show that the influence of the IMF on the plasma convection in the magnetosphere as given by the new model is consistent with observations. The tail field is modified to be consistent with the interconnection field.