Electric Discharge

When a large amount of charge has accumulated on the metal sphere of the Van de Graaff generator, we can produce some very strong fields and high voltages. We can estimate the voltage by bringing a grounded sphere up to the Van de Graaff generator as shown in Figure (1). A voltage of about 100,000 volts is required to make a spark jump about an inch through air. Thus if
we get a spark about 2 inches long between the Van de Graaff generator and the grounded sphere, we have brought enough charge onto the generator sphere to create a voltage of about 200,000 volts. (The length of the sparks acts as a crude voltmeter!)
As an exercise, let us estimate how many coulombs of charge must be on the Van de Graaff generator sphere to bring it up to a voltage of 200,000 volts.

Figure 1: We can discharge the Van de Graaff generator by bringing up a grounded sphere as shown. Since about 100,000 volts are required to make a spark one inch long, we can use the maximum length of sparks to estimate the voltage produced by the Van de Graaff generator.
Outside the Van de Graaff generator sphere, the electric field is roughly equal to the electric field of a point charge. Thus the voltage or electric potential of the sphere should be given by Equation (1) as

......(1)

where r is the radius of the Van de Graaff generator sphere. (Remember that r is not squared in the formula for potential energy or voltage.)
Let us assume that r = 10 cm or .1 m, and that the voltage V is up to 200,000 volts. Then Equation (1) gives

A couple millionth’s of a coulomb of charge is enough to create 200,000 volt sparks. As we said earlier, a whole coulomb is a huge amount of charge!