# Potential over the surface of a charged conductor

Potential over the surface of a charged conductor

Where static electricity is concerned, the potential is the same an over a charged conductor, no matter how the charge or charges may be distributed over it. Thus, in the experiment illustrated in Fig. 33.3 (a) the negatively charged rod produces a potential difference between the ends of the insulated conductor AB. Immediately, however, this potential difference causes some free electrons in the conductor to move towards the end B, with the result that the potential becomes equalized all over
the conductor.

This fact may be tested by attaching a length of copper wire to the cap of an electroscope. The wire is then wound once or twice round a polythene rod to serve as an insulating handle, and the free end of the wire is moved all over the surface of the conductor. No matter where the wire touches the surface of the conductor, the leaf divergence remains the same, showing that the potential is the same all over the surface. fn the same manner it may be shown that the potential is everywhere the same over the surface of a charged pear-shaped conductor (Fig. 33.3 (b)). The reader

should compare this experiment very carefully with the experiment to investigate the distribution of charge over the surface of such a conductor, described on page 373 The two experiments make it clear that, although the charge is unequally distributed, the potential is uniform orer the surface. (See also Fig. 33.4.) It is important to understand the two different methods of using the electroscope in these experiments. When charge is transferred to the electroscope by means of the proof plane the leaf potential, and hence its divergence, will depend on the quantity of charge transferred. Since the capacitance (see below) of the electroscope is constant, its potential, and hence its leaf divergence, will be a measure of the charge placed on it.
On the other hand, if the electroscope is connected to a conductor by a wire the two effectively become a single conductor, and the leaf divergence will indicate their common potential.