Charge Q is distributed between two paraticles. What should be the value of charges on the particles so that the repulsive force acting between them is maximum?

Explanation

Let charge on one particle is q and that on the other particle is (Q - q) if the distance between them is r then force acting between them,
`F=(q(Q-q))/(4pi in_(0)r^(2))`
Value of F is maximum for a given value of q, for that value of q,
`(dF)/(dq)=0`
`therefore (dF)/(dq)=(1)/(4pi in_(0)r^(2))*(d)/(dq)(Qq-q^(2))=0`
or, ` (1)/(4pi in_(0)r^(2))*(Q-2q)=0 or, Q-2q=0`
`therefore q=(Q)/(2)`