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Question

# Two charged spherical conductors of radii R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2) is

A
R21R22
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B
R1R2
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C
R2R1
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D
(R1R2)
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Solution

## The correct option is C R2R1 When two conductors are connected by a conducting wire, then the two conductors should have the same potential. So, V1=V2 ⇒14πε0Q1R1=14πε0Q2R2 ⇒14πε0Q1R1×R1R1=14πε0Q2R2×R2R2 ⇒Q1R14πR21=Q2R24πR22 ⇒σ1R1=σ2R2 (∵σ=Q/A) ∴σ1σ2=R2R1 Hence, option (C) is correct.

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