8_Example_ch II-Diwakar Karuppiah
Channel: P6 Scholars Academy
Date: 2020-06-30

Twenty seven drops of same size are charged at 220V. They coalesce to from a bigger drop. Calculate the potential of the bigger drop.
Solution:
 Let radius of each small drop =r
 Radius of large drop                =R
Then      4/3 𝜋𝑅^3=27×4/3 𝜋𝑟^3
      or                 R = 3r
potential of each small drop,
   𝑉=1/〖4𝜋𝜀〗_0 .𝑞/𝑟
∴  Total charge on 27 drops,
               Q = 27, q = 27 ×〖4𝜋𝜀〗_0r V

Potential of large drop, 
𝑉=1/〖4𝜋𝜀〗_0 .𝑄/𝑅=1/〖4𝜋𝜀〗_0 . (27 ×〖4𝜋𝜀〗_0 r V)/3r
=9𝑉=9×220=1980𝑉.