Why charge distribute equally when two identical conductor touch each other? I have surf this question on the internet but I did not get any good explanation. Basically they have shown that charged distributes equally to make the potential of the two spheres equal. But i have a problem in understanding this. Suppose two identical conductor A and B is brought close to each other. Conductor A has charge equal to +q and Conductor B has charge equal to +Q When Conductor A touch the Conductor B, dont the conductor A induces negative charges on B and similarly conductor B induces negative charge on A. then how does the electron move to make the charge equal on both the conductors?

 A: I will provide the generic picture of how things work in electrostatics and if this does not deal with your concerns, please let me know in the comments, so that I can edit my answer.
First of all, you have to keep in mind that you are studying electrostatic problems and electrostatic problems alone. This means that you want no charges flowing throughout the conductors, as this is a more complicated problem that is not usually studied in the context of introductory electromagnetism courses. When the two conductors touch, then they must be viewed as one (composite) body. The latter body is also a conductor. This means that the electric field on the bulk of the composite body must be zero, as it is for the bulk of any conductor. If this were not the case, then the non-zero electric field would exert (non-zero) electric force on charges and then they would move. For that reason the electric field is zero in the bulk of conductors and hence there can be no charge inside that bulk, as they would create a non-zero electric field.
So, if two conductors touch, then we expect the total charge distribution to respect the aforementioned result. Furthermore, if they do touch, then the contact surface belongs in the bulk of the conductor. Since no electric field must be developed there, there is no change in the potential (since $\Delta V=-\int \vec{E}\cdot d\vec{r}$) and hence the potential is constant along this surface.
Now, to answer your question on how are the charge going to be distributed along the surfaces of the two spheres, in order for the electric field to be zero inside the composite conductor, charge must be transfered from the most positively charged sphere (assume $Q,q>0$) to the less positively charged sphere. The reason is simply because you want to have no net charge in the contact surface. In addition, you want the total charge $Q+q$ to be distributed on the surface of the composite conductor, so you can think of the problem as having one conductor with charge $q+Q$ and determie how the charge is going to be distributed there.
I hope this makes sense... If not, please do not hesitate to ask, so that I can edit my answer.
