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A point like charge Q is placed inside the cavity of a spherical conductor of an internal radius R1 and external radius R2 initially neutral(uncharged) (see the figure), the question is how is the charge distribution of the induced charge Q1 and Q2?

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the solution in the book says: in order to determine the distribution of the charge sigma2 of Q2 on the external surface , we can observe that according to the electrostatic shielding this distribution is independent of the charge distribution sigma1 of the charge Q1 on the surface R1 and of the position of the point like charge Q , but at the same time the distribution of the induced charge Q1 will not be uniform unless the point charge Q is placed in the center of the sphere.

Can someone explain me what does this mean?

Qmechanic
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Ama Ouchen
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1 Answers1

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The charge distribution on the surfaces occurs in such a way that the potential on every point is same (it's a conductor). Since the charge is at a different distance from the points on the inner surface, the distribution has to be non uniform to make potential same at every point. Now draw a gaussian surface outside the inner surface but inside the outer surface. The net charge inside this surface is zero. So no electric field line crosses this surface. Resultant, the inner charge distribution doesn't affect the distribution on the outer surface. This is "electrostatic shielding". So the charge distribution on the outer surface is independent of the distribution on the inner surface and presence of charge. Hence the charge distribution on the outer surface is uniform since charge gets distributed uniformly on a conductor surface in absence of any charge affecting it.

Ankur Singh
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