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Closed Conducting Shell

We have seen that there are no excess charges inside a conductor. That is, the material inside a conductor is electrically neutral. If some substance is removed from inside a conductor, a close cavity is created. Creating a cavity inside the conductor does not change the field anywhere. If there are no charges within the cavity, the electrical field in it equals to zero. It means that the external charges, including the charges on the outer surface of the conductor, do not create any electric field in the cavity. This forms the basis of electrostatic shielding. Measuring instruments are often shielded or screened from the influence of any external field, by keeping them in a cavity inside a conductor. In practice, the solid conducting shell can be replaced by a dense metallic grating (net).

A closed conducting shell divides the entire space into the inner and outer parts, which are completely independent of one another in respect of electric fields. It means that any arbitrary displacement of charges inside the shell does not introduce any change in the field of the outer space and hence the charge distribution on the outer surface of the shell remains unchanged.

A point charge q within a cavity in a conductor induces equal and opposite charges on the surface of the cavity and on the surface of the conductor. If the charges outside the conductor are displaced, the field inside the cavity is not affected, and hence the distribution of the charges inside the cavity as well as the distribution of the charges induced on the cavity walls remains unchanged. A point charge q is within an electrically neutral shell whose outer surface has spherical shape. Find the potential V at the point P lying outside the shell at a distance b from the centre O of the outer surface.

The field at point P is determined only by charges induced on the outer spherical surface. The field due to the point charge q and that due to the charges induced on the inner surface of the sphere is equal to zero everywhere outside the cavity. In view of symmetry, the charges on the outer surface of the shell are distributed uniformly. For any point outside the sphere, the distributed charge q behaves as if whole charge is concentrated at the centre O.

Hence, Potential at P: V =

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