Question

Objects A, B and C are three identical, spherical conductors. Originally A and B both have charges of +3 mC, while C has a charge of –6 mC. Object A and C are allowed to touch, then they are moved apart. Then objects B and C are allowed to touch, and they are moved apart.

If Object A and B are now held near each other, they will

• A. attract
• B. repel
• C. have no effect on each other
• D. First attract to a certain position then repel

Answer 1

The correct option is A

attract

When two similar conductors touch they exchange charges such that each end up with half of the total charge they initially possessed.So this is like three brothers A, B, C (or sisters if you will) who have an understanding among themselves. Whenever any two of them meet they add the total money(in this case charges) they have and divide that in half among each other (except for imagine that they can have negative money ) Initially,

A B C

+3 mC +3 mC -6 mC

When A and C are allowed to touch

A C

[+3 mC + (-6 mC) = -3 mC

(Note that –3 mC is charge on the A and C together)

When moved apart

$A\iff C\frac{-3mC}{2}\frac{-3mC}{2}$

Charge on C = $\frac{-3mC}{2}$ and

Charge on B = +3 mC

Similarly, when B and C are together

$+3mC+\left(\frac{-3}{2}mC\right)=+\frac{3}{2}mC$

When moved apart

$B\iff C\frac{+3}{4}mC\frac{+3}{4}mC$

Hence if A $\left(\frac{-3}{2}mC\right)$ and B $\left(\frac{+3}{4}mC\right)$ are brought close to each other

What should they do? Yes, attract