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Question

# Eight charged liquid drops each of radius 1mm and charge 0.1nC, merge together to form a bigger drop. The electric potential at the surface of single big drop is:

A
3.6kV
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B
7.2kV
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C
1.8kV
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D
36kV
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Solution

## The correct option is B 3.6kVLet, the density of liquid =Sgiven, radius =1×10−3m charge =0.1nc let mass =xNow, as we know, S=massvolumeThe radius of the bigger drop is given by R.and for small drop, S=x(43πr3)⇒r3=x43πSFor bigger drop, S=8x(43πR3)⇒R3=8x43πSSo, R3r3=8⇒R3=8x3⇒R=2r⇒R=2×10−3m; charge on the bigger drop is given by, Q=8×0.1nc =8×10−10CPotential on the surface is determined as,=KQR=9×109×8×10−102×10−3=3.6kV∴ Option A is the correct answer.

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