Electric Potential at Single Charged Conductor

Electric Potential at Single Charged Conductor

The electric potential at a point due to a charge is measured by the work done in bringing unit positive charge from infinity to that point. This electric potential is measured in volts and plays important role in determining capacitance in a circuit which is defined as charge (q) per unit potential (V).

Consider a long straight cylindrical conductor placed in uniform medium such as air as shown in the Fig. 1.25.1.

It carries a charge along its entire length given by + q coulombs per meter. The electric flux lines of this charged conductor are radial and uniformly placed. The points which are equally placed from this conductor are at same potential and have the same flux density (D).

Let us obtain electric flux density at a distance x from the conductor i.e. along cylindrical surface of radius x meters.

The electric flux density on the surface is equal to the flux leaving the conductor per meter of length divided by the surface area in an axial length of 1 m with radius x meters.

If D is divided by the permittivity of the medium (e) the we get electric field intensity (E). 

As x approaches ∞, the value of E approaches zero. Thus the potential difference between conductor and neutral plane at infinity distance where E and potential is zero, is given by,

Review Question

1. Explain electric potential at single charged conductor.