# 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?

• if the balls are small enough (ie can be represented as points) then 0 will be correct as there can be no separation between the induced positive and negative charges – danimal Apr 22 '15 at 15:13
• Since your question ends with the phrase "correct answer", the answer to this MCQ which would be deemed "correct", depends on the level of the textbook/course. While your reasoning about induction is correct, you are almost certainly over-thinking this if this happens to be a MCQ in introductory electrostatics. Again, you are not overthinking it if the course actually taught you enough EM to calculate the effects of induction. But if you are looking for the physically correct answer, then you are right, there would be an attraction due to induction (small as it may be). – 299792458 Apr 22 '15 at 18:24