The figure shows a solid metal sphere at the center of a hollow metal sphere. As

Question

The figure shows a solid metal sphere at the center of a hollow metal sphere. Assume that E=1.6

The figure shows a solid metal sphere at the center of a hollow metal sphere. Assume that E=1.6 times 104N/C. no title provided What is the total charge on the exterior of the inner sphere? Express your answer with the appropriate units. What is the total charge on the inside surface of the hollow sphere? Express your answer with the appropriate units. What is the total charge on the exterior surface of the hollow sphere? Express your answer with the appropriate units

Explanation / Answer

This is just an application of Gauss' Law. So

a) If we set up a spherical, Gausian surface with a radius of 8cm from the center sphere ie at the point where the E-field = 1.3 * 10^4 N/C, then, using Gauss' law, we have

E * 4(pi) r^2 = Q/eo

where Q is the total charge inside the Gausian surface

Q = eo * E * 4(pi) r^2 = 9.0 * 10^9 * 1.3 * 10^4 * 4 * pi * 0.08^2 = 9.4 * 10^12 C

b) The charge in the surface of the inner sphere will induce an equal, opposite charge in the inside wall of the shell. So the charge in the inner wall is (- 9.4 * 10^12 C)

c) Since there can be no E-field in the wall of the shell [ otherwise charges would move], then the concentration of negative charge in the inner wall will leave a deficit of electrons on the surface of the shell ie the charge on the outer surface of the shell will be +9.4 * 10^12 C

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