81. Electrical capacitance of the isolated conductor

If the charges on the conductor are in equilibrium, all parts of the conductor have the same potential. This allows an important characteristic of the electrical properties of a conductor to be entered - electrical capacitance, or, as is often said, simply capacitance.

Let's consider a conductor of any shape, sufficiently remote from all other bodies ( isolated). Potential on infinity consider equal to zero. Then the not charged conductor will also have zero potential.

At delivery to a body of charge \(Q\) in surrounding space appears an electric field. The potential of the conductor will change and become equal to \(V\). If a conductor to delivery still the same charge \(Q\), then the potential of it will become equal \(2\,V\), as between the charge and the potential according to \((8-24)\) exists directly proportional dependence. No relation of the charge of a body to its potential does not depend on the quantity of the charge and is determined by the properties of the conductor itself. Electrical capacitance conductor \(C\) is the quantity, numerically equal to the relation of the charge \(Q\), delivered to the conductor, to its potential \(V\).

\( C \,= \,\frac{Q}{V} \) (8-26)

The term "electrical capacitance" is adopted by analogy from the capacity of a vessel. The higher the capacitance of the conductor, the less its potential changes when the charge is delivered. Similarly, the larger the capacity of a vessel, the less the liquid level changes when a certain amount of liquid is added.