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Physics Question on electrostatic potential and capacitance

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

A

8:01

B

4:01

C

2:01

D

1:08

Answer

4:01

Explanation

Solution

Radius of bigger drop (8)1/3r=2r(8)^{1/3} r = 2r. Total charge = 8q8q. Potential of bigger drop = 8q/4πε0 R=8 q/4 π ε0(2r)=4[q/4 π ε0 r]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.