# Heat liberated after connecting two plates

1. Feb 7, 2013

### Saitama

1. The problem statement, all variables and given/known data
(see attachment)

2. Relevant equations

3. The attempt at a solution
When the switch is open, the charges on the plates will rearrange and the final charges would be as shown in attachment 2. The energy stored due to the electric field between the plates (sorry if I said it incorrectly) is $U=\frac{1}{2}ε_o E^2 \cdot (Ad)$, where E is the electric field between the plates. Solving I get, $U=\frac{q^2d}{2Aε_o}$. I don't know how to proceed from here.

Any help is appreciated. Thanks!

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2. Feb 7, 2013

### TSny

You need to determine how the charges will be arranged after the switch is closed. What do you think would happen in the figure of attachment 2 if you connected a wire from the inside surface of the left plate to the inside surface of the right plate?

Note that the expression for U that you gave is only for the energy of the field between the plates before the switch is closed. There would also be energy in the field outside the plates before the switch is closed. (Far away form the plates the field will be similar to a point charge of charge 4q.) But don't worry about that for now.

3. Feb 7, 2013

### Saitama

That's something I am having trouble with. Its been long I have touched this.

The charges rearrange again?

4. Feb 7, 2013

### TSny

Yes, when the switch is closed there is some rearrangement of the charge.

5. Feb 7, 2013

### Saitama

I still can't think of any equation that would help me to find the final charges.

6. Feb 7, 2013

### TSny

Can you use symmetry to decide on the total final charge for each plate?

7. Feb 7, 2013

### Saitama

Still clueless. :(

Would the charges be 2Q and 2Q on each plate?

8. Feb 7, 2013

### TSny

Yes. By symmetry the plates end up with the same net charge and the total charge in the system must be conserved.

9. Feb 7, 2013

### Saitama

lol, that was just a wild guess. Can you teach me how can I find the value of final charges in a proper manner?

10. Feb 8, 2013

### Saitama

Anyone?

11. Feb 8, 2013

### sankalpmittal

Well, according to me you have to use symmetry only. When switch is closed, there will be no net transfer of charges and charges on both side parallel plates will be same. This is because of established charge equilibrium between two plates, and coulomb law of conservation of charge is obeyed.

12. Feb 8, 2013

### haruspex

If the charges are not equal, there will be a potential difference, so a current will flow in a direction tending to equalise them. To answer it rigorously, you would have to assume a certain set of circuit characteristics (resistance, induction, capacitance), find the equations of state, and show that as time tends to infinity it converges to equal charge. In the real world, just assume a steady state is reached.

13. Feb 8, 2013

### Saitama

Thanks haruspex! What should be my next step? Find the charges on each side of plate?

14. Feb 8, 2013

### Dick

Well, yes. Did you derive the charges on each side of the plate? Or was that given to you? Do you agree the charges will equalize on each plate?

15. Feb 8, 2013

### Saitama

Before closing the switch?
I do know that the charges flow until the plates are at same potential but can't really form an equation to find the final charges. :uhh:

16. Feb 8, 2013

### Dick

Let's bypass the other questions for now. If you agree the plates are at the same potential after the switch is closed, what's the E field between them after the switch is closed?

17. Feb 8, 2013

### Saitama

How? I don't have the final charges to find the electric field.

18. Feb 8, 2013

### Dick

You don't need to. The E field is the gradient of the potential between the two plates, right? If they are at the same potential, what does that mean? If you want to backtrack you can certainly find the charge on the inner surface between the two plates if you need to.

19. Feb 8, 2013

### Saitama

Oh yes, there would no electric field between the plates.

I think I have got it but what about the energy TSny pointed out in his post #2. Don't I need to worry about that?

20. Feb 8, 2013

### haruspex

Yes, you need to determine the drop in potential energy. What's the energy of the E field when the charges are equal?