The potential due to Q is constant upto radius R and so cancels out in the difference! This means that if we now connect the smaller and larger sphere by a wire, the charge q on the former FIGURE . Illustrating the principle of the electrostatic generator. Van de Graaff generator, principle and demonstration: will immediately flow onto the matter, even though the charge Q may be quite large.
The natural tendency is for positive charge to move from higher to lower potential. Thus, provided we are somehow able to introduce the small charged sphere into the larger one, we can in this way keep piling up larger and larger amount of charge on the latter. The potential (Eq. .
) at the outer sphere would also keep rising, at least until we reach the breakdown field of air. This is the principle of the van de Graaff generator. It is a machine capable of building up potential difference of a few million volts, and fields close to the breakdown field of air which is about × V/m. A schematic diagram of the van de Graaff generator is given in Fig.
. . A large spherical conducting shell (of few metres radius) is supported at a height several meters above the ground on an insulating column. A long narrow endless belt insulating material, like rubber or silk, is wound around two pulleys – one at ground level, one at the centre of the shell.
This belt is kept continuously moving by a motor driving the lower pulley. It continuously carries positive charge, sprayed on to it by a brush at ground level, to the top. There it transfers its positive charge to another conducting brush connected to the large shell. Thus positive charge is transferred to the shell, where it spreads out uniformly on the outer surface.
In this way, voltage differences of as much as or million volts (with respect to ground) can be built up. SUMMARY . Electrostatic force is a conservative force. Work