There is one charged tiny spherical oil drop and the magnitude of electric field intensity at a point on its surface is E. If n such drops are combined to make a single drop then what will be the net electric field intensity at a point on the surface of the bigger spherical drop. Assume that charge is uniformly distributed over the volume of oil drop.

Let q be ths charge contained in small oil drop of radius r .

 

Electric field E = K × ( q / r² )  ............................... (1)

 

where K = 1/ ( 4πε_o ) is Coulomb's constant and ε_o is permittivity of free space

 

If n drops are joined together , then total charge Q = ( n q )

 

Let ρ be the density of oil 

 

Volume of final oil drop formed from n small drops is given as

 

(4/3)πR³ ρ = n (4/3)πr³ ρ  ................................(2)

 

where R is radius of final oil drop

 

FRom eqn.(2) , we get ,  R = n^1/3 r 

 

Electric field on the surface  of Final oil drop , E^' = K × ( q / R² ) = K × [ ( nq ) / ( n^2/3  r² ) ]

 

E^' = n^1/3 × K × ( q / r² ) = n^1/3  × E