Gauss\'s law applied to spherical conducting shells... The figure shows a spheri

Question

Gauss's law applied to spherical conducting shells...

The figure shows a spherical conducting shell, inner radius a, and outer radius b, with a point charge +Q inside. In case (1) the point charge is at the center of the shell, and in case (2) it is off-center. Use Gauss's law to predict the charge on the inner surface and on the outer surface of the shell in each case. In each case, describe the electric field in the three regions r < a, a < r < b, and r > b. In the figures, draw a typical electric field line starting from the charge, extending vertically in the diagram, and ending where you think it should end.

https://www.dropbox.com/s/78uzvk06yx7m25f/01-figure.jpg?dl=0

Explanation / Answer

When charge is given to conductor , it spreads uniformly over its outer surface, wheather it is at the center or not.
So +Q charge will distributed over the surface.due to induction –Q will induced on inner surface
From fig- due to induction +Q charge will induce on outer surface.
(a) E .F for r<a
E = 0
[Since all the charge is on surface. Then from gauss’s law
E .ds = Q/ E0
Q = 0 , E = 0
Or      inside a conductor E.F = 0
(b)   For a< r< b
E. ds = Q/ E0
E = Q/ 4*pie*r2 E0
(c) For r> b
E = 0
Since no charge enclosed by surface

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