Problem on distribution of charges between charged/uncharged spheres

[frostchaos123]

Homework Statement

2 Spherical conductors B and C having equal radii and carrying equal charges repel each other with force F. Another conductor A having same radius as B but uncharged is brought into contact with B, and then C and then removed from both.

Find the new force of repulsion between B and C. (Answer should be 3F/8)

Homework Equations

Coulomb's law

The Attempt at a Solution

Since when an uncharged sphere A contacts with B, the charges from B flow over, leaving B with half of the charges, and A with half of the charges (initial assumption).

Afterwards charged A contacts C, but i am not quite sure about the distribution of charges from here on. Since now A have half of the original charges, does it mean that 1/4 of the charges of C will flow into A to equalise?

Or is my initial assumption that A will get half of the charges from B wrong in the first place?

Any help is much appreciated.

 

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I think the charge is going to equalise. So you can just add the charge of A and C and divide it by 2 to get the total charge on each one.

So, let's say A has 0 and B and C have Q.
A touches B so they both have Q/2.
A touches C. The charge distributes equally. So, total charge is 3Q/2. So, there will be 3Q/4 on each one.
So, you're right.