Let two identical spheres have charge q. And distance between them
=r∴ Force between the spheres
(F)=‌Now when an identical uncharged sphere
C comes in contact with
A, charge
q on sphere A get's divided equally to both sphere.
So, both sphere
A and
C have charge
=‌Now, C get's in contact with B. So their total charge
(q+‌) gets divided equally.
So, charge on both
B and
C is
=‌=‌Now,
C is place midpoint between
A and
B.
Repulsion force between A and C,
FAC=‌=‌Repulsion force between B and C,
FBC=‌=‌∴ Net force on C,
Fnet=FBC−FAC=‌−‌=‌(‌−‌)=‌×‌ =‌F[. as
F=‌]