Distribution of Potential and Charge over the Surface of a Closed Conductor

Figure 4. Distribution of charge on a pear-shaped closed conductor

Potential

A pear shaped closed surface conductor as shown in Figure 4. is charged. If wire connected to a gold leaf electroscope is contacted with the surface of the conductor, the electroscope shows a constant deflection. This indicates that the potential on the surface of the conductor is constant all over the surface.

Charge

The charge around the conductor is measured using a proof plane.The proof plane is a small brass disc on an insulated handle. It is first Earthed to ensure there is no charge on the disc. The proof plane is then touched onto the surface of the conductor. The proportion of charge acquired by the disc when it is touched onto the surface of the conduction is proportional to the surface charge density of conductor. The charge can be measured by touching the brass disc of the proof plane on the inside of a metal can standing on the top of the cap of a gold leaf electroscope. The deflection is an indication of the charge at the surface at that point.

If this process is repeated at various positions on the conductor it is found that the least charge is found where the radius of curvature of the conductor is greatest and that the charge is greatest where the surface of the conductor has the smallest radius of curvature, i.e. where it is most pointed. If the radius of curvature is very small, the density of charge can be large enough for charge leakage to occur creating a wind of ions.

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