At a distance r between their centres, the magnitude of the
electrostatic force on each is given by
F
rqq
=
′
41
0
2
πε
neglecting the sizes of spheres A and B in comparison to r When an
identical but uncharged sphere C touches A, the charges redistribute
on A and C and, by symmetry, each sphere carries a charge q/2 Similarly, after D touches B, the redistributed charge on each is
q¢/2 Now, if the separation between A and B is halved, the magnitude
of the electrostatic force on each is
′ =
′
=
′ =
F
q
q
r
rqq
F
41
2
2
2
41
0
2
0
2
π
π
ε
ε
( / )(
( / )/ )
(
)
Thus the electrostatic force on A, due to B, remains unaltered