Question

Two uncharged conductors, A and B, are of different sizes. They are charged as follows:
1. A is charged from an electrostatic generator to charge q.
2. A is briefly touched to B.
3. Steps 1 and 2 are repeated until the charge on B reaches a maximum value.
If the final charge on B is 3q, what was the charge on A after the first time it touched B?
Why is the answer q/4?

Answer 1

the key principle is that when you charge up a conductor the charges on it will distribute itself such a way to keep the vector sum of all E's inside of it zero. When you touch the two conductors it becomes one large conductor and the principle still stays the same. Since at the end of the process B will have the maximum 3q and A will have q with electric field zero inside the large conductor, then if you reduce the total surface charge density evenly by the factor of 4, electric field would end up remaining zero inside the large conductor. This is why A will have only (1/4)q after the first contact and (3/4)q on B.