The sum of charge on two point charges is Q.What should be the values of charges on them for a maximum force between them for a given separation?

Explanation

Given: `q_(1)+q_(2)=Q`
or `q_(2)=Q-q_(1)`
Force between the two point charges
`F=(Kq_(1)(Q-q_(1)))/(d^(2))` where Q and d are constants.
For a maximum force
`(dF)/(dq_(1))=0`
`(dF)/(dq_(1))=K[q_(1)(-1)+(Q-q_(1))(q)]=0`
i.e. `-q_(1)+Q=q_(1)=0`
or `Q=2q_(1)`
`:.q_(1)=Q/2` and `q_(2)=Q/2`