Finding number of charges using Coulomb's Law

[Dr. Who]

Homework Statement

Please refer to the image; problem-1. My theory is that there are two spheres 'A' and 'B', where 'A' is (partially and primarily) positively charged, and 'B' is (partially and primarily) negatively charged. The magnitude of negative charge is greater than the positive charge. After the spheres are in contact, negative charge from 'B', equal to the magnitude of positive charge on 'A', is transferred to sphere 'A' to balance it. The negative charge on sphere 'A' (due to induction) and leftover negative charge on 'B' are now responsible for repulsion between 'A' and 'B'. I think there is one more equation required concerning the composition of charges in the system, before and after the electrical contact. Please help!

Homework Equations

F = k[Q_A][-Q_B] / r² → ①

where, (assuming )
Q_A is the initially excess positive charge on sphere 'A'
Q_B is the initially excess negative charge on sphere 'B'

F' = k[-Q`_A][-Q_B + Q_A] / r² →②

Where,
-Q`_A is the net negative charge on sphere 'A'
[-Q_B + Q_A] is the net negative charge left on sphere 'B' after a negative charge equal to magnitude of Q_A is transferred to sphere 'A'.

The Attempt at a Solution

[/B]
Solving equation ① using given values;
3.003 x 10^-12 = [Q_A][-Q_B]

Solving equation ②;
1.001 x 10^-12 = [-Q`_A][-Q_B + Q_A]

 

[Simon Bridge]

Your problem statement is incomplete: you left out what you are supposed to find. I guess it must be in the attachment where almost nobody will read it.

But let's just do some quick translation:
A and B are charged spheres - the language suggests that the spheres are conducting, both positive and negative charges are present on both spheres, and net charges are given as below. (There is no such thing as "partially charged" ...an object is either charged or it is not.)
A has charge q and B has charge -Q so that Q,q > 0, and Q>q

When in contact, charge is free to flow between the spheres.
Charge flows in both directions.

Using the above notation:
Net charge on A+B (touching each other) is going to end up as ... what?
If the spheres are otherwise equal, then we'd expect the charge on each sphere to be ... what?

When does induction normally apply?