A charge is divided into two charges q and (Q-q) .The value of q so that force between them is maximum is equal to

Explanation

Let q and Q -q be the charge given to the point charges . Then the force between them will be :
`F=1/(4piepsilon_0)(q(Q-q))/r^2`
Let x=q(Q-q)
`rArr (dx)/(dq)=Q-2q=0 rArr q=Q//2`
`rArr (d^2x)/(dq^2)=-2`
Hence, for q=Q/2 , x will be maximum .F is proportional to x, and hence F is maximum when q=Q/2 .Therefore , the charges will experience a maximum force when total charge is equally divided between the two.