Question

Discuss the operation of and resulting electric fields from the Van der Graaff generator. Include in your answer an explanation of where the excess charge originates and how it is gathered to form a charge at the output. You should use diagrams to explain your answer and of the resulting electric field around the generator’s sphere.

Answer 1

A simple Van de Graaff generator consists of a belt of rubber (or a similar flexible dielectric material) moving over two rollers of differing material, one of which is surrounded by a hollow metal sphere. Two electrodes, (2) and (7), in the form of comb-shaped rows of sharp metal points, are positioned near the bottom of the lower roller and inside the sphere, over the upper roller. Comb (2) is connected to the sphere, and comb (7) to ground. The method of charging is based on the triboelectric effect, such that simple contact of dissimilar materials causes the transfer of some electrons from one material to the other. For example (see the diagram), the rubber of the belt will become negatively charged while the acrylic glass of the upper roller will become positively charged. The belt carries away negative charge on its inner surface while the upper roller accumulates positive charge. Next, the strong electric field surrounding the positive upper roller (3) induces a very high electric field near the points of the nearby comb (2). At the points, the field becomes strong enough to ionize air molecules, and the electrons are attracted to the outside of the belt while positive ions go to the comb. At the comb (2) they are neutralized by electrons that were on the comb, thus leaving the comb and the attached outer shell (1) with fewer net electrons. By the principle illustrated in the Faraday ice pail experiment, i.e. by Gauss's law, the excess positive charge is accumulated on the outer surface of the outer shell (1), leaving no field inside the shell. Electrostatic induction by this method continues, building up very large amounts of charge on the shell.

In the example, the lower roller (6) is metal, which picks negative charge off the inner surface of the belt. The lower comb (7) develops a high electric field at its points that also becomes large enough to ionize air molecules. In this case, the electrons are attracted to the comb and positive air ions neutralize negative charge on the outer surface of the belt, or become attached to the belt. The exact balance of charges on the up-going versus down-going sides of the belt will depend on the combination of the materials used. In the example, the upward-moving belt must be more positive than the downward-moving belt. As the belt continues to move, a constant "charging current" travels via the belt, and the sphere continues to accumulate positive charge until the rate that charge is being lost (through leakage and corona discharges) equals the charging current. The larger the sphere and the farther it is from ground, the higher will be its peak potential. In the example, the wand with metal sphere (8) is connected to ground, as is the lower comb (7); electrons are drawn up from ground due to the attraction by the positive sphere, and when the electric field is great enough the air breaks in the form of an electrical discharge spark (9). Since the material of the belt and rollers can be selected, the accumulated charge on the hollow metal sphere can either be made positive (electron deficient) or negative (excess electrons).

The friction type of generator described above is easier to build for science fair or homemade projects, since it does not require a high-voltage source. Greater potentials can be obtained with alternative designs (not discussed here) for which high-voltage sources are used at the upper and/or lower positions of the belt to transfer charge more efficiently onto and off the belt.

A Van de Graaff generator terminal does not need to be sphere-shaped to work, and in fact, the optimum shape is a sphere with an inward curve around the hole where the belt enters. A rounded terminal minimizes the electric field around it, allowing greater potentials to be achieved without ionization of the air, or other dielectric gas, surrounding. Outside the sphere, the electric field becomes very strong and applying charges directly from the outside would soon be prevented by the field. Since electrically charged conductors do not have any electric field inside, charges can be added continuously from the inside without increasing them to the full potential of the outer shell. Since a Van de Graaff generator can supply the same small current at almost any level of electrical potential, it is an example of a nearly ideal current source.