Induction in Electrostatics While solving some problems on electrostatics, I came across this question :

Two balls carrying charges of +3 $\mu C$ and -3$\mu C$ attract each other with a force $F$. If a charge of +3$\mu C$ is added to both the balls, the force between the balls will be
A. 2$F$
B. $F$
C. $F$/2
D. Zero

Out of these, the obvious option seems to be zero, as the charge on one ball cancels out, and this is the answer given in the solution. But on deeper thought, I realized that the charged ball could still attract the neutral ball through the phenomenon of induction. So, the answer should not be zero. Am I thinking correctly? And if I am, then what could be the correct answer?
 A: In this question the force F has to be calculated using coulomb's law.In coulomb's law it clearly states that both  the 02 bodies should be charged.So in this question one will gain charge up to 6 uC and the other will be zero.So there will be no force between them.
The question has not mentioned whether the two balls are insulators or conductors.It should probably be insulators.that's why the force was zero.
But certain insulators can be charged by induction. Then the force between them is not due to electrostatic force but due to the polarization of insulator molecules.
For example, running water from a tap can be bent if you keep a charged rod (say a charged  plastic comb).Water is neutral and the rod has a charge.But still it bends.It is because water is a polar molecule and that the like charges between the molecule and the rod repel while unlike charges attract.
A: Induced charges are possible only if the balls are conductors. Maybe the balls are insulators, in which case the force between them is zero.
