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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 | 31 Jul, 2021, 19:12: PM
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 | 31 Jul, 2021, 19:30: PM

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