1
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Question

# A conducting sphere of radius 10cm is charged with 10μC. Another uncharged sphere of radius 20 cm is allowed to touch it for sometime, after that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

A
1:1
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B
2:1
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C
1:3
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D
4:1
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Solution

## The correct option is B 2:1After touch if the common potential is V, according to charge conservation Q=C1V+C2V here Q=10μC and C1,C2 are the capacitances of two sphere.or V=QC1+C2After touch the charge on first sphere is Q1=C1V=C1QC1+C2 and charge on second sphere is Q2=C2V=C2QC1+C2Charge densities are σ1=Q1S1=C1V4πr21 and σ2=Q2S1=C2V4πr22Thus, σ1σ2=C1C2×r22r21=4πϵ0r14πϵ0r2×r22r21=r2r1=20/10=2/1 as the capacitance of isolated sphere =4πϵ0R

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