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Three concentric spherical metallic shel...

Three concentric spherical metallic shells A, B and C of radii a, b and c (a lt b ltc) have surface charge densities `sigma`, `-sigma` and `sigma` respectively.
`(i) Find the potential of the three shells A, B and C.
(ii) If the shells A and C are at the same potential, obtain the relation between the radii a, b and c.

Text Solution

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`V_A=(sigmaa)/epsilon_0-(sigmab)/epsilon_0+(sigma_c)/epsilon_0`
`=sigma/epsilon_0(a-b+c)`
`=V_B=((sigmaa)/epsilon_0)(a/b)-(sigmab)/epsilon_0+(sigmac)/epsilon_0`
`=sigma/epsilon_0[a^2/b-b+c]`
`V_C=((sigmaa)/epsilon)(a/c)-((sigmab)/epsilon_0)(b/c)+(sigmac)/epsilon_0`
`=sigma/epsilon_0(a^2/c-b^2/c+c)`
c. `W_(ArarrC)=0`
or `(a-b+c)=((a^2-b^2)/c)+c`
or `a+b=c`
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