Limitations on Charging a Conductor and Concept of Capacitance

Limitations on Charging a Conductor

How much electric charge a conductor can hold?
As more charge Q is transferred to a conductor, its electric potential V becomes higher making it increasingly difficult to add more charge. It is similar to the case of pumping air in a tank where, the more air is pumped into the tank, the pressure opposing the flow of additional air becomes higher making it difficult to pump more air.

Suppose we keep on transferring more and more charge to a conductor. As charge on the conductor increases, both the field intensity and the potential at its surface keep on increasing. There is a limit, however, to the field strength which can exist on a conductor without ionising the surrounding air. When this happens, the surrounding air essentially becomes a conducting medium and any additional charge placed on the conductor will leak off to the air. This threshold value of the electric field strength for which a material loses its insulation properties is known as the dielectric strength of that material.

Above discussion concludes that the quantity of charge that can be put on a conductor is limited by the surrounding dielectric medium (such as air). One more factor affecting the amount of charge that can be placed on a conductor is size and geometry of the conductor. Smaller conductors can usually hold less charge. The shape of a conductor also influences its ability to retain charge. The sharper portions (the regions of higher curvature) of the conductor have higher charge accumulation and field intensity in these regions may be sufficiently high to ionise the local air. It is necessary to remove all sharp edges from an electrical equipment to minimise the leakage of charge.

Concept of Capacitance

Capacitance of a conductor is a measure of its ability to store charge on it.
When a conductor is charged its potential rises. It is found that for an isolated conductor (conductor should be of finite dimension, so that potential at infinity can be assumed to be zero), potential of the conductor is proportional to the charge given to it.

We get C = q/V. Thus, capacitance of a conductor can be defined as charge required to increase the potential of the conductor by 1 unit. It represents the capacity of the conductor to hold charge per unit voltage.

Important points about Capacitance

It is a scalar quantity and its SI unit is C/V (Coulombs per volt) also called Farad.
Its dimensional formula is M⁻¹L⁻²T⁴I².
If for each 1C charge transferred to a conductor, its potential increases by 1V, the conductor is said to have a capacitance of 1 Farad (1F).
1F is a very large value of capacitance. Practically, the conductors or capacitors normally have capacitance in the order of μF or nF.
Capacitance of an isolated conductor depends on following factors: shape and size of the conductor, surrounding medium and presence of other conductors.
Capacitance of a conductor is independent of charge (Q) on the conductor, potential (V) of the conductor and energy (U) stored by the conductor.

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