Nanographite materials show novel electronic properties: spin glass like behaviors [1], the on/off switching of magnetism with molecule adsorptions [2], and so on. Here, we study electronic states in nanographite ribbons with zigzag edges. Effects of the nearest neighbor Coulomb interactions are investigated using the extended Hubbard model. The nearest Coulomb interactions stabilize a novel electronic state with the opposite electric charges separated and localized along both edges, resulting in a finite electric dipole moment pointing from one edge to the other. Next, electric capacitance is calculated to examine nano functionalities. We find that the behavior of the capacitance is widely different depending on whether the system is in the magnetic or charge polarized phases. In the magnetic phase, the capacitance is dominated by the presence of the edge states while the ribbon width is small. As the ribbon becomes wider, the capacitance remains with large magnitudes as the system develops into metallic zigzag nanotubes. It is proportional to the inverse of the width, when the system corresponds to the semiconducting nanotubes and the system is in the charge polarized phase also. The latter behavior could be understood by the presence of an energy gap for charge excitations.