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A spherical conducting shell of inner ra...

A spherical conducting shell of inner radius `r_1` and outer radius `r_2` has a charges 'Q' A charges 'q' is placed at the centre of the shell.
What is the surface charges density on the (i) inner surface (ii) outer surface of the shell?
(b) A spherical conducting shell of inner radius `r_1` and outer radius `r_2` has a charges 'Q' A charges 'q' is placed at the centre of the shell.
Write the expression for the electric field at a point ` x gt r_2` from the centre of the shell.

Text Solution

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Let us have a conducting shell of inner radius `r_1 ` and outer radius `r_2` . When it is given a charge Q, the charge spreads on its outer surface and there is no charge on inner surface of shell. When a charge q is placed at the centre of the shell, it indducess a charge -q on inner surface 1 of the shell and a charge +q on outer surface 2 of the shell.
(i) The surface charge density on the inner surface
` sigma _1= ( -q)/( 4pi r_1^(2)) `
(ii) The surface charge density on the outer surface
` " "sigma _2= +( Q+q)/( 4 pi r_2^(2)) `
` (##U_LIK_SP_PHY_XII_C01_E09_026_S01##) `
(b) For a point lying outside the spherical shell`( x gt r_2) `. Electric field E is given by
` " " E = ("Total charge on spherical shell")/( 4 pi in_0 x^(2)) =(Q+q)/( 4 pi in_0 x^(2)) `
` (##U_LIK_SP_PHY_XII_C01_E09_026_S01.png" width="80%">
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