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.

Asked by jangraarti2 | 31st Jul, 2021, 07:12: PM

Expert Answer:

Let q be ths charge contained in small oil drop of radius r .
 
Electric field E = K × ( q / r2 )  ............................... (1)
 
where K = 1/ ( 4πεo ) is Coulomb's constant and εo 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)πRρ = n (4/3)πr3 ρ  ................................(2)
 
where R is radius of final oil drop
 
FRom eqn.(2) , we get ,  R = n1/3 r 
 
Electric field on the surface  of Final oil drop , E' = K × ( q / R2 ) = K × [ ( nq ) / ( n2/3  r2 ) ]
 
E' = n1/3 × K × ( q / r2 ) = n1/3  × E 

Answered by Thiyagarajan K | 31st Jul, 2021, 07:30: PM