  Using the Harmonic map ansatz, we reduce the axisymmetric, static
Einstein-Maxwell equations coupled with a magnetized perfect fluid to a set of
Poisson-like equations. We were able to integrate the Poisson equations in
terms of an arbitrary function $M=M(\rho,\zeta)$ and some integration
constants. The thermodynamic equation restricts the solutions to only some
state equations, but in some cases when the solution exists, the interior
solution can be matched with the corresponding exterior one.
