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We consider a relativistic, degenerate electron gas at zero-temperature underthe influence of a strong, uniform, static magnetic field, neglecting any formof interactions. Since the density of states for the electrons changes due tothe presence of the magnetic field (which gives rise to Landau quantization),the corresponding equation of state also gets modified. In order to investigatethe effect of very strong magnetic field, we focus only on systems in which amaximum of either one, two or three Landau level(s) is/are occupied. This isimportant since, if a very large number of Landau levels are filled, it impliesa very low magnetic field strength which yields back Chandrasekhar's celebratednon-magnetic results. The maximum number of occupied Landau levels is fixed bythe correct choice of two parameters, namely the magnetic field strength andthe maximum Fermi energy of the system. We study the equations of state ofthese one-level, two-level and three-level systems and compare them by takingthree different maximum Fermi energies. We also find the effect of the strongmagnetic field on the mass-radius relation of the underlying star composed ofthe gas stated above. We obtain an exciting result that, it is possible to havean electron degenerate static star, namely magnetized white dwarfs, with a masssignificantly greater than the Chandrasekhar limit in the range 2.3-2.6M_Sun,provided it has an appropriate magnetic field strength and central density. Infact, recent observations of peculiar Type Ia supernovae - SN 2006gz, SN2007if, SN 2009dc, SN 2003fg - seem to suggest super-Chandrasekhar-mass whitedwarfs with masses up to 2.4-2.8M_Sun, as their most likely progenitors.Interestingly our results seem to lie within the observational limits.

Strongly magnetized cold electron degenerate gas: Mass-radius relation of the magnetized white dwarf