`10^(6)` small identical drops of water, all charged to the same potential, are combined to form a single large drop. If E is the sum of the electrostatic energy of each small drop, find the energy of large drop.

Options

A. `10^(-4)` E
B. E
C. `10^(6)` E
D. `10^(4)` E

Answer

D

Explanation

Energy of one drop `= 1/2 CV^(2) = 1/2 qV`
where q = CV is the charge of one drop, C is the capacitance.
Energy of `10^6` drops,
`E = 1/2 qV 10^(6)`
Potential on the combined drop = (potential of each initial drop)
= (potential of each initial drop) `xx (n^(2//3))`
`V. = V(10^(6))^(2//3) = 10^(4) V`
Energy of combined drop,
`E. = 1/2 q.V. = 1/2 (10^(6) q)V.`
`= 10^(6)` E
`therefore E. = 10^(4)` E