How does charge redistribute when three spheres are connected and separated?

[albert611]

Hello, I have a question about redistributing charges. If you have three identical spheres: A is -2 uc (microcoulombs), B is -6 uc, and C is +5 uc, touch A and B together, separate, then touch B and C together, and separate, with what charge does C end up with? I don't understand how positive and negative charges can necessarily divide their charge (as in B+C). Thank you very much!

-Albert

 

[Galileo]

If the spheres are perfect conductors, all the charge will distrubute among 2 spheres will touch each other equally, since they are identical.
So if two spheres touch, you can view it essentially as single conductor. When you separate them, the total charge will be evenly distributed over the two spheres.

 

[HallsofIvy]

Just add: two negatives will give a "larger" negative, two positives will give a larger positive, opposite signs will cancel.
Here, A and B have a total of (-2)+ (-6)= -8 uc so after touching an separating, each will have -4 uc.

NOW B and C have a total of (-4)+ (+5)= +1 uc so after touching and separating, each will have a charge of +0.5 uc.

 

[xanthym]

Of course, the working assumption here is that all the spheres have equal radii. The answer would change if this were not the case. When 2 spherical conductors of unequal radii are "connected", the net charge distributes itself such that the Potential is equal throughout both conductors. To attain this equal Potential, the larger sphere would require greater total (surface) charge than the smaller sphere, hence producing an unequal charge distribution between the spheres.