Question

The collector sphere, or dome, of a Van de Graaff generator builds a net charge of 4.5 x 10-3 C. Determine the magnitude of the electric field at various locations. Hint: Review the properties of conductors in electrostatic equilibrium and use Gauss's law. Assume a spherically symmetric distribution of charge on the collector sphere. a. Determine the magnitude of the electric field inside of the collector sphere. E = N/C b. Determine the magnitude of the electric field at the surface of the collector sphere assuming that is has a radius of 11.5 cm. E= N/C c. Determine the magnitude of the electric field at a distance of 1 m from the center of the collector sphere. E= N/C

Answer 1

a)

charge enclosed by the inside the dome

q = 0

using gauss law

E. (4 pi r^2) = 0 /eo

E = 0 N/C

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b)

as per gauss law

E* ( 4 pi * 0.115^2) = 4.5* 10^-3 / ( 8.85* 10^-12)

E = 3.061* 10^9 N/C

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c)

for any outside point sphere and shell acts as point charge

again

E ( 4 pi 1^2) = 4.5* 10^-3 / ( 8.85* 10^-12)

E = 4.05* 10^7 N/C

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