We consider a relativistic , degenerate electron gas at zero-temperature under the influence of a strong , uniform , static magnetic field , neglecting any form of interactions .
Since the density of states for the electrons changes due to the presence of the magnetic field ( which gives rise to Landau quantization ) , the corresponding equation of state also gets modified .
In order to investigate the effect of very strong magnetic field , we focus only on systems in which a maximum of either one , two or three Landau level ( s ) is/are occupied .
This is important since , if a very large number of Landau levels are filled , it implies a very low magnetic field strength which yields back Chandrasekhar ’ s celebrated non-magnetic results .
The maximum number of occupied Landau levels is fixed by the correct choice of two parameters , namely the magnetic field strength and the maximum Fermi energy of the system .
We study the equations of state of these one-level , two-level and three-level systems and compare them by taking three different maximum Fermi energies .
We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above .
We obtain an exciting result that , it is possible to have an electron degenerate static star , namely magnetized white dwarfs , with a mass significantly greater than the Chandrasekhar limit in the range 2.3 - 2.6 M _ { \odot } , provided it has an appropriate magnetic field strength and central density .
In fact , recent observations of peculiar Type Ia supernovae - SN 2006gz , SN 2007if , SN 2009dc , SN 2003fg - seem to suggest super-Chandrasekhar-mass white dwarfs with masses up to 2.4 - 2.8 M _ { \odot } , as their most likely progenitors .
Interestingly our results seem to lie within the observational limits .