Charge `Q` is divided into two parts which are then kept some distance apart . The force between them will be maximum if the two parts are

Options

A. `Q//4`, `3Q//4`
B. `Q//3`, `2Q//3`
C. `Q//2`, `Q//2`
D. `Q//5`, `4Q//5`

Explanation

Let us place a quantum of charge `'q'` on the first sphere, so we have charge `(Q-q)` on the other sphere.
The force of attraction between the spheres is
`F=((Q-q)q)/(4piepsilon_(0)d^(2))`
`(dF)/(dq)=(1)/(4piepsilon_(0)d^(2))[Q-q)-q]=0`
`:. q=Q//2`
`:. (C )`