Chapter 26, Problem 24P

The Van de Graaff generator, diagrammed in Figure P26.24, is an electrostatic device that can raise the metal dome to a high voltage. The dome of such a generator is seen on the left in Figure 22.1a. In the device, charge is delivered continuously to the high-potential dome by means of a moving belt of insulating material. The belt is charged at point Ⓐ by means of a discharge between comb-like metallic needles and a grounded grid. The needles are maintained at a positive electric potential of typically 10⁴ V. The positive charge on the moving belt is transferred to the dome by a second comb of needles at point Ⓑ. Because the electric field inside the dome is negligible, the positive charge on the belt is easily transferred to the dome from its interior regardless of its potential. Suppose the generator is operating so that the potential difference between the high potential dome Ⓑ and the charging needles at Ⓐ is 15.0 kV. Calculate the power required to drive the belt against electrical forces at an instant when the effective current delivered to the dome is 500 μA.

Figure P26.24