Electrostatic potentials and voltages

The electric potential, V, is defined as the potential energy per unit positive test charge. Thus, for the case of a planar charge distribution, 

In a more general situation where the electric field is position-dependent, the differential change in electric potential dV over a differential vector distance dr is given by 

The voltage is a quantity closely related to the quantity defined above as the electric (or electrostatic) potential V. Strictly speaking, the voltage is a difference in electrostatic potential, but it is often taken as simply the 

The differential capacitance, C ff, of a capacitor is defined as the magnitude of the differential charge transfer, dQ, from one plate to the other divided by the change, dV, in electric potential produced by this 

Consider a case in which the field is uniform within the capacitor, as it is in the example of a parallel-plate capacitor discussed above. In that example 

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