Magnetospheric convection occurs in response to a combination of factors. It is driven by the solar wind-magnetosphere interaction, causes Joule heating in the ionosphere, and energizes particles as they convect earthward. While the equation governing magnetospheric convection under the quasi-static condition is well known, there is a lack of a formal proof that the energy processes named above are properly balanced in the convection formalism. In particular, the question has not been answered concerning the conservation of energy in a steady state convection. In this paper, I prove that energy conservation holds for steady state convection of an isotropic plasma. The consideration of energetics also sheds light on the nature of and relationship between region 1 and region 2 currents. It is further proven that the quasistatic convection formalism is conformal invariant, a property which can be exploited to develop more efficient algorithms for modeling magnetospheric convection. Several examples are presented to illustrate the conformal transformation method. ¿ American Geophysical Union 1996