Question

a charge q is divided into two parts q1 and q - q1 what is ratio of q/q1 so that force between two parts placed at a given distance is maximum​

Answer 1

Force is given as :

F = k(q1)(q-q1)/d² ..............(1)

Now, differentiation w.r.t q1

=> dF/d(q1) = k/d² { q - 2(q1)} .........(2)

Put 1st order derivative to zero.

=> dF/d(q1) = k/d² { q - 2(q1)} = 0

=> q1 = q/2

=> q/q1 = 2

So , ratio is 2.