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

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

Electrostatic Potential and Capacitance

Solution:

Radius of bigger drop $(8)^{1/3} r = 2r$. Total charge = $8q$. Potential of bigger drop = $8_q/4\pi \varepsilon_0\, R = 8 \, q/ 4 \, \pi \, \varepsilon_0 (2r) = 4 [q/4 \,\pi\, \varepsilon_0\, r]$ = 4 times the potential of single drop.