Two conducting spheres of radii r and 3r initially have charges 3q & q respectively. Their separation is much larger their radii. If they are joined by a conductor of high resistance, the force between them will :

Options

A. increase continuously
B. decrease continuously
C. first increase, then decrease
D. first decrease, then increase

Answer

C

Explanation

Let charge on smaller sphere be x and on larger sphere be `4q -x`
force between them is given by
`F=(kx(4q-x))/(d^(2))`
`(dF)/(dx)=0rArr 4q -2x =0`
`rArr x = 2q (d^(2)F)/(dx^(2))=(K)/(d^(2))(-2)lt 0`
It represents a maximum
Final charges on the smaller sphere and the larger sphere are q & 3q respectivelt as required by the equality of potentials
`:.` force will increase until the charges becomes equal and after that force will decrease