Question 19.7: A demonstration Van de Graaff generator has a 25.0 cm diamet...

College Physics[EXP-4825]

A demonstration Van de Graaff generator has a 25.0 cm diameter metal sphere that produces a voltage of 100 kV near its surface. (See Figure 19.7.) What excess charge resides on the sphere? (Assume that each numerical value here is shown with three significant figures.)

Strategy
The potential on the surface will be the same as that of a point charge at the center of the sphere, 12.5 cm away. (The radius of the sphere is 12.5 cm.) We can thus determine the excess charge using the equation

$V=\frac{k Q}{r}$ . (19.41)

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Solving for Q and entering known values gives

$Q=\frac{r V}{k}$ (19.42)

=\frac{(0.125 m )\left(100 \times 10^{3} V \right)}{8.99 \times 10^{9} N \cdot m ^{2} / C ^{2}}

$=1.39 \times 10^{-6} C =1.39 \mu C$ .

Discussion
This is a relatively small charge, but it produces a rather large voltage. We have another indication here that it is difficult to store isolated charges.

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