Question

Please try to solve this question in detail. I myself tried to solve this question but I am not able to understand it's charge distribution.so please try to give detailed solution

Thanks in advance

Answer 1

Three large plates are arranged as shown as shown in the figure. How much charge will flow through the key "K" if it is closed ?

2. Relevant equations&
3. The attempt at a solution
For solving this I thought that On the first plate charge Q will be distributed as Q/2 & Q/2 on the either sides. And on the second plate charge 2Q will be distributed as Q & Q on the either sides. Now induction will take place due to the higher charge Q on the lower magnitude charge. Hence -Q will generate on the the right side of 1st plate and + Q on its right side and on the third plate -Q on the left side and + Q on the right side.
Now 1 and three are connected and charge will flow from 1 to another.

inner sides of 1st and 2nd plate should have same but opposite signs. Let 2nd plate has
(Q + x) and 1st plate has (Q/2 - y) charges. These charges should be equal. It is giving the equation : x + y = - Q/2.

Now the outer side of 2nd plate will have (Q/2 + y) charge due to conservation of charge. And the right side of plate 2 will have (Q - x) charge.
Induction will also take place on the 3 rd plate. It'll have -(Q-x) and (Q-x) on the left and right sides.
When the key becomes close the inner charges will remain at the same condition due to iteration of the opposite charges. But the outer charges of the 1st and 3rd plate will move for to make the potential equal. Now I am stuck in this situation how the charge will flow now?
Even if I get another equation It'll be easy to solve the equations but no positive outcome.

Please Please Please friends help me in completing this. I am in the big confusion here.

The answer of this question is 5Q/6.