What is the Charge Transfer Process between Two Charged Balls in Electrostatics?

[luiseduardo]

Homework Statement

The ball 1 can be charged to a certain charge Q by a generator. After that, through contact with the ball 2, the first ball can transfer to second ball part of its charge. After the first contact, the ball 2 has a charge q. Before the contact, the ball 2 was neutral. What charge the ball 2 can acquire repeating the process repeatedly.

http://www.luiseduardo.com.br/electricity/electrostatics/electrostaticsproblems_arquivos/image002.jpg

Homework Equations

Q = Q'+q --> Conservation of Charges
Q = C.V ---> Capacitor charge
C = r/K ----> Capacitance of a sphere

The Attempt at a Solution

Well, first, I tried to use the conservation of charges equation several times replacing Q' (charge of the sphere that will be recharged) by C.V, where C is the capacitance and V the potential. After that, I didn't find a way to find the answer of the problem. Could anyone help me? Please give me your complete explanation or solution.

PS: The answer of the problem is qQ/(Q-q)

Thanks.

 

[Adithyan]

The charge from one ball to another ball will flow till they are at the same potential.
Now, to give you a start, let me tell you the first step:

Assume C1 and C2 as the capacitances of ball 1 and ball2 respectively, equate the potential and find the ratio of $\frac{C1}{C2}$. Now equate the potential for the 2nd step till you find a relation between the charges transferred.

P.S: 1) The charges will be a part of a series. it is for you to guess which one.
2) It is against the rule of this forum to give a detailed solution. Moreover, I think you should try
your fullest before you look for the solution.

Best of luck!

ADI.