Electrical Engineering ⇒ Topic : Potential of a Charged Conducting Sphere

Potential of a Charged Conducting Sphere

Consider an isolated conducting sphere of radius r metres placed in air and charged uniformly with Q coulombs. The field has spherical symmetry i.e. lines of force spread out normally from the surface and meet at the centre of the sphere if produced backward. Outside the sphere, the field is exactly the same as though the charge Q on sphere were concentrated at its centre.

(i) Potential at the sphere surface. Due to spherical symmetry of the field, we can imagine the charge Q on the sphere as concentrated at its centre 0 [See Fig.(1)]. The problem then reduces to find the potential at a point r metres from a charge Q.

                             (1)                                                                 (2)

                                                              figure

Potential at the surface of sphere

(2) Potential outside the sphere. Consider a point P outside the sphere as shown in Fig.(2). Let this point be at a distance of D metres from the surface of sphere

(3) Potential inside the sphere. Since there is no electric flux inside the sphere, electric intensity inside the sphere is zero.

Hence, all the points inside the sphere are at the same potential as the points on the surface.