  We propose an analytical model based on the solution of the
magnetohydrodynamics (MHD) equations for studying the origin of intrinsic
magnetospheres. For this purpose, we reveal a new gauge condition for the
electromagnetic vector potential, which eases the solution of such complex
system of non-linear equations. Using this model, we analyse the deformation of
the terrestrial magnetic field due to the presence of the solar wind. By
comparing with experimental observations, we have found that the geometrical
configuration of the magnetosphere, before, and after the magnetic field of the
Earth started to deviate the solar wind, has not changed notably, and that the
solar wind should have had a finite conductivity. This model can also be used
to perform linear stability analysis of fluid and magnetic instabilities.
