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14/09/2021 10:51 am
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Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2) is:
(1) \(\frac{R_1}{R_2}\)
(2) \(\frac{R_2}{R_1}\)
(3) \(\sqrt{(\frac{R_1}{R_2})}\)
(4) \(\frac{R_1^2}{R_2^2}\)
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14/09/2021 10:58 am
Correct answer: (2) \(\frac{R_2}{R_1}\)
Explanation:
For a conducting sphere
E = \(\frac{\sigma}{\in_0}\)
V = \(\frac{\sigma R}{\in_0}\)
as both spheres have same potential after connecting with wire,
V1 = V2
σ1R1 = σ2R2
⇒ \(\frac{\sigma_1}{\sigma_2}\) = \(\frac{R_2}{R_1}\)