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Question

# Eight small drops, each of radius r and having same charge q are combined to form a big drop. The ratio of potential of the bigger drop to the smaller drop is

A
8:1
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B
4:1
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C
2:1
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D
1:8
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Solution

## The correct option is B 4:1When 8 small drops are combined to a single drop, let Q be charge and R be radius of drop after coalesce. Net charge Q=8q Final volume =8× initial volume. 4πR3=8×4πr3 R3=8r3 R=2r Potential of a sphere of charge Q and radius R is V=Q4πϵ0R Ratio of potentials VbigVsmall=QR×rq VbigVsmall=8q2r×rq=4

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