Chapter 23, Problem 84GP

A Van de Graaff generator (Fig. 23–41) can develop a very large potential difference, even millions of volts. Electrons are pulled off the bell by the high voltage pointed electrode at A, leaving the bell positively charged. (Recall Example 23−5 where we saw that near sharp points the electric field is high and ionization can occur.) The belt carries the positive charge up inside the spherical shell where electrons from the large conducting sphere are attracted over to the pointed conductor at B, leaving the outer surface of the conducting sphere positively charged. As more charge is brought up, the sphere reaches extremely high voltage. Consider a Van de Graaff generator with a sphere of radius 0.20 m. (a) What is the electric potential on the surface of the sphere when electrical breakdown occurs? (Assume V = 0 at r = ∞.) (b) What is the charge on the sphere for the potential found in part (a)?

FIGURE 23–41

Problem 84.

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