The purpose of this thesis is to obtain more realistic equations of state to describe the matter forming magnetized white dwarfs, and use them to solve its structure equations. The equations of state are determined by considering the weak magnetic field approximation $B<B_c$ ($B_c=4.41times10^{13}text{ G}$) for the electron gas of the star. The magnetic field introduces anisotropic pressures, even for the moderate values present in white dwarfs. Also, we consider the energy and pressure correction due to the Coulomb interaction of the electron gas with the ions located in a crystal lattice. Moreover, spherically symmetric Tolman-Oppenheimer-Volkoff structure equations are solved independently for the perpendicular and parallel pressures, confirming the necessity of using axisymmetric structure equations, more adequate to describe the anisotropic system. Therefore, we study the solutions in cylindrical coordinates. In this case, the mass per longitude unit is obtained instead of the total mass of the white dwarf.
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