`n` charged drops, each of radius `r` and charge `q`, coalesce to from a big drop of radius `R` and charge `Q`. If `V` is the electric potential and `E` is the electric field at the surface of a drop, then.

Options

A. `E_(big) = n^(2//3) E_(small)`
B. `V_(big) = n^(1//3) V_(small)`
C. `E_(small) = n^(2//3) E_(big)`
D. `V_(big) = n^(2//3) V_(small)`

Answer

d

Explanation

D `Q = n q, R = n^(1//3) r`
`E_(small) = (k q)/(r^2), E_(big) = (kQ)/(R^2)`
`E_(big) = (k n q)/(n^(2//3)) r^2) = (n^(1//3) (k q)/(r^2) = n^(1//3) E_(small)`
`V_(small) = (k q)/( r), V_(big) = (k Q)/( R)`
`V_(big) = (k n q)/(n^(1//3) r) = n^(2//3) (k q)/( r) = n^(2//3) V_(small)`.