Question

a charge q is to be distributed on two conducting sphere what should be valueof charges on sphere so that repulsive forces b/w them is max. when they are placed at fixed dist. from each other in air

Answer 1

Simplyforce depends on product of their charges as distance b/w them is fixed. And product of charges will be maximum when they are equal (by am gm)
q1+q2/2>= √q1q2
So value of charges should be q/2 on each

Answer 2

Answer:

The charge is distributed over two conducting spheres with the distances between them as given as fixed, the maximal value is attained by –

When the charge is of equal magnitude on both the conducting spheres, then only the repulsive force between them will be maximum as the force of electrostatics either attractive or repulsive is the product of charge ratio to distance with constants.

Therefore, distance being fixed, the equal charges will have maximum product therefore the charge q be equally distributed as q / 2 on each of conducting sphere.