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A spherical conducting shell of inner radius r_1and 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_1and 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 pointx gt r_2 from the centre of the shell. |
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Answer» Solution :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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