  The effect of magnetic fields in the Equations of State (EoS) of compact
objects is the splitting of the pressure in two components, one parallel and
the other perpendicular to the magnetic field. This anisotropy suggests the
necessity of using structure equations considering the axial symmetry of the
magnetized system. In this work, we consider an axially symmetric metric in
spherical coordinates, the $\gamma$-metric, and construct a system of equations
to describe the structure of spheroidal compact objects. In addition, we
connect the geometrical parameter $\gamma$ linked to the spheroid's radii, with
the source of the anisotropy. So, the model relates the shape of the compact
object to the physics that determines the properties of the composing matter.
To illustrate how our structure equations work, we obtain the mass-radii
solutions for magnetized White Dwarfs. Our results show that the main effect of
the magnetic field anisotropy in White Dwarfs structure is to cause a
deformation of these objects. Since this effect is only relevant at low
densities, it does not affect the maximum values of magnetized White Dwarf's
masses, which remain under Chandrasekhar limit.
