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A metallic sphere of radius R is charged to a potential V. If is brought in contact with an uncharged metallic sphere of radius R/2 and then separated. Then potential of the smaller sphere will be

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V/4

V/3

2V/3

3V/4

answer is A.

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Detailed Solution

Initial charge on the larger sphere $Q = 4 π \in_{o} R . V$

$∴$ potential of the smaller sphere $V' = \frac{Q}{C_{1} + C_{2}} = \frac{4 π \in_{o} RV}{4 π \in_{o} R + 4 π \in_{o} R / 2} \Rightarrow V' = 2 V / 3$ .

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