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Charging of graphene by magnetic field and mechanical effect of magnetic oscillations

We discuss the fact that quantum capacitance of graphene-based devices leads to variation of it's charge density under changes of external magnetic field.The charge is conserved, but redistributes to substrate or other graphene sheet. We derive exact analytic expression for charge redistribution in the case of ideal graphene in strong magnetic field. When we account for impurities and temperature, the effect decreases and the formulae reduce to standard quantum capacitance expressions. The importance of quantum capacitance for potential Casimir force experiments is emphasized and an application of atomic force microscope technique for measurement of density of states is proposed.