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The effect of an inhomogeneous magnetic field,which varies inversely with distance on the ground state energy level of graphene,is studied.We analytically show that graphene under the influence of a magnetic field aris-ing from a straight long current-carrying wire(proportional to the magnetic field from carbon nanotubes and nanowires)exhibits zero-energy solutions and find that contrary to the case of a uniform magnetic field for which the zero-energy modes show the localization of electrons entirely on just one sublattice corresponding to a single valley Hamiltonian,zero-energy solutions in this case reveal that the probabilities for the electrons to be on both sublattices,say A and B,are the same.