Van De Graaff Generator

This is a machine that can build up high voltages of the order of a few million volts. The resulting large electric fields are used to accelerate charged particles (electrons, protons, ions) to high energies needed for experiments to probe the small scale structure of matter.

The principle underlying the machine is as follows. Suppose a large spherical conducting shell of radius R, on which we place a charge Q. This charge spreads itself uniformly all over the sphere.

The field outside the sphere is just that of a point charge Q at the centre; while the field inside the sphere vanishes. So the potential outside is that of a point charge; and inside it is constant, namely the value at the radius R. We thus have: Potential inside conducting spherical shell of radius R carrying charge Q is equal to constant.

 Suppose that in some way we introduce a small sphere of radius r, carrying some charge q, into the large one, and place it at the centre. The potential due to this new charge clearly has the following values at the radii indicated:

Potential due to small sphere of radius r carrying charge q

 Taking both charges q and Q into account we have for the total potential V and the potential difference the values

Assume now that q is positive. We see that, independent of the amount of charge Q that may have accumulated on the larger sphere and even if it is positive, the inner sphere is always at a higher potential: the difference V(r)–V(R) is positive. 

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 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. The potential at the outer sphere would also keep rising, at least until we reach the breakdown field of air.

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 3 × 106 V/m.

Construction of Van de Graff generator

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 6 or 8 million volts (with respect to ground) can be built up.