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Question
Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has 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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Solution
Since, the two spheres are at the same potential, therefore
`1/(4piε_0) q_1/R_1 = 1/(4piε_0) q_2/R_2` ⇒ `R_1/ε_0 q/(4piR_1^2) = R_2/ε_0 q_2/(4piR_2^2)`
or `sigma_1R_1 = sigma_2R_2` ⇒ `sigma_1/sigma_2 = R_2/R_1`
As R2 > R1, this imply that σ1 > σ2.
The charge density of the smaller sphere is more than that of the larger one.
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