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Consider two conducting spheres of radii R_(1) and R_(2) with R_(1) gt R_(2).If the two are at the same potential, the larger sphere bas more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one. |
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Answer» SOLUTION :Both spheres have same POTENTIAL `:. V_(1) = V_(2)` `:. (kq_(1))/(R_(1))=(kq_(2))/(R_(2))` `:. (q_(1)R_(1))/(4piR_(1)^(2))= (q_(2)R_(2))/(4piR_(2)^(2))` (` because ` Dividing by 4 pi on both SIDES ) `sigma_(1) R_(1) = sigma_(2) R_(2) [ because sigma= (q)/(4piR^(2))]` Now `R_(1) gt R_(2)` `sigm_(1) lt sigma_(2)` SECOND Method : Charge on larger sphere is more than charge on smaller sphere Now `(kq_(1))/(R_(1)) = (kq_(2))/(R_(2))` `[becauseq = sigmaA] ` and `k = (1)/(4piin_(0))` `(sigma_(1)A_(1))/(4piin_(0)R_(1))=(sigma_(2)A_(2))/(4piin_(0)R_(2))` `:. (sigma_(1)xx4piR_(1)^(2))/(4piin_(0)R_(1))=(sigma_(2)xx4piR_(2)^(2))/(4piin_(0)R_(2))` `:. (sigma_(1)R_(1))/(in_(0))= (sigma_(2)R_(2))/(in_(0))` `:. (sigma_(1))/(sigma_(2))=(R_(2))/(R_(1))` but `R_(1) gt R_(2) implies 1 gt (R_(2))/(R_(1))` `(sigma_(1))/(sigma_(2)) lt 1` `:. sigma_(1) lt sigma_(2)` `:.` Charge DENSITY of smaller sphere is less than that of larger sphere . |
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