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

We discuss the fact that the quantum capacitance of graphene-based devices leads to variation of graphene charge density under changes of external magnetic field. The charge is conserved, but redistributes to the substrate or other graphene sheets. We derive an exact analytic expression for charge redistribution in the case of ideal graphene in a strong magnetic field. When we account for impurities and temperature, the effect decreases and the formulas reduce to standard quantum capacitance expressions. The importance of quantum capacitance for potential Casimir force experiments is emphasized and the corresponding corrections are worked out.