Suppose that in your physics class, a van de Graaff generator (see the Figure 22

Question

Suppose that in your physics class, a van de Graaff generator (see the Figure 22.27 in the textbook) with a sphere radius of 11.0 cm is producing sparks 8 inches long. Assume that on a humid day, an electric field of 2.00×104 N/C at the surface of the sphere is enough to produce sparks about an inch long.

1. Use Gauss's law to calculate the amount of charge stored on the surface of the sphere before you bravely discharge it with your hand.(q = ? C)
2.Assume all the charge is concentrated at the center of the sphere, and use Coulomb's law to calculate the electric field at the surface of the sphere. (E = ? N/C)

Explanation / Answer

Given that electric field E = 2.00*10^4 N /C The electric field required to produce a sparks 8 inches long is 8 times as strong as the field needed to produce the spark E = 8 ( 2.00*10^4 N /C )      = 16.0*10^4 N /C a)   the amount of charge stored on the surface of the sphere is      q = _0 E (4r^2 )          = ( 8.85*10^-12 )( 16.0*10^4 N/C) (4 (0.11m)^2          = 21.5*10^-8 C b) From columbs law          E = k q / r^2               = (9.00*10^9 ) ( 21.5*10^-8 C) / (0.11m)^2                = 15.9*10^4 N/C

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