1.

A total charge Q is distributed over two concentric hallow uniform sphere of radii a and b, (bgta) such a way that their surface charge densities are qual. The potential at the common centre is given by :

Answer»

`(Q)/(4piepsilon_(0))((a+b))/((a^(2)+b^(2))`
`(Q)/(4piepsilon_(0))((a-b))/((a^(2)+b^(2))`
`(Q)/(4piepsilon_(0))((a-b))/((a+b)^(2))`
`(Q)/(4piepsilon_(0))((b-a))/((a+b)^(2))`

Solution :`(Q')/(4pia^(2))=(Q-Q')/(4pib^(2))`
`Q'b^(2)=QA^(2)-Q'a^(2)`
`Q'=(Qa^(2))/(a^(2)+b^(2))`
`(KQ-Q')/(b)+(kQ')/(a)`
`(K)/(b)[Q-(Qa^(2))/(a^(2)+b^(2))]+k[(Qa)/(a^(2)+b^(2))]`
`(kQ(b+a))/(a^(2)+b^(2))`


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