# Earthing of a System of Parallel Metal Plates

1. Jan 9, 2016

### gracy

whenever any plate of system of parallel plates is earthed total charge on outer faces of the plates will become zero .Is it always true?or only in case of system of two plates?

2. Jan 9, 2016

### QuantumQuest

Can you elaborate on what system you're talking about - maybe with a small diagram?

3. Jan 9, 2016

### Mister T

When electrostatic demonstrations are first presented to students, the demonstrator will often touch a piece of conducting material to the ground (earth) and declare that the excess charge has been removed. In fact, though, what has happened is that the potential has been set, by definition, to zero. Usually, but not always, this means that the excess charge has been removed. In the case of an isolated conductor, it's true that the excess charge has been removed, but if there are other charged objects nearby, the grounded conductor can still retain some excess charge. In this case we refer to it as induced charge.

A capacitor is a pair of conductors.

4. Jan 9, 2016

### gracy

the note he writes is it applicable for system of any number of plates (three four and so on)?

5. Jan 9, 2016

### QuantumQuest

If you have a third, fourth plate and so on, when you earth the second for instance as is done in the video, then is there going to be any flux from second to third anymore? and so on. If you earth another plate in the sequence then the same pattern holds for its adjacent plate and so on.

6. Jan 9, 2016

### TSny

Yes, it's true for any number of parallel, infinite plates. No matter what the initial charges are for the plates and no matter which plate you ground, there will be no final charge on the left surface of the left-most plate and no charge on the right surface of the right-most plate.

7. Jan 9, 2016

### gracy

And no matter what kind of the charge is on the outer surfaces of last plates?I mean whether these surfaces are positively charged or negatively charged .

8. Jan 9, 2016

### TSny

Yes. Before you ground one of the plates, you can have any charge you want on the plates (positive or negative). After grounding one of the plates, the outer surfaces of the first and last plates will have zero charge.

9. Jan 9, 2016

### gracy

Thank you so much

10. Jan 9, 2016

### gracy

Even if left most plate and right most plates are grounded?

11. Jan 9, 2016

### TSny

Yes.

12. Jan 9, 2016

### gracy

from time 0-0.54
why q1=q6=half of the total charge?

13. Jan 9, 2016

### cnh1995

I did the math and ended up with q1+q6=Qtotal. Mathematically, there are 6 unknowns but only 5 simultaneous equations. So, q1=q6 must have some physical significance. Are they metal plates?

14. Jan 9, 2016

### cnh1995

Consider just Y and Z, both uncharged. If 10μC charge is put on Y, it will distribute as 5μC on right surface and 5μC on left surface(uniform distribution). This will induce -5μC on the left surface of Z and +5μC on the right surface. Now, if Y is made neutral again and -8μC charge is placed on Z, there will be -4μC on the left surface of C and -4μC on the right surface(uniform distribution again). So, you can see if 10μC is placed on Y and -8μC is placed on Z at the same time, on Y there will be 9μC on the right and 1μC on the left(sum of placed charge+induced charge) and on Z, there will be -9 on the left surface and +1 on the right surface.
This must be the reason why the charges on the outermost surfaces are equal. It's the sum of supplied charge (which distributes uniformly) and induced charge. Interesting! Try and see if you can extend the logic for 3 plates. Give charge to one plate and calculate the induced charges on the other two plates and repeat this for 3 times(one for each plate). Then just add the supplied charge and induced charge on each plate and you'll see the outermost surfaces have equal charge.

Last edited: Jan 9, 2016
15. Jan 9, 2016

### Staff: Mentor

One way to think about it is that the fields produced by a collection of charges tries to move the net charge to the extremities of the system. It's why a charge on an isolated plate ends up on the two outer surfaces, half on each one, or why the charge on a spherical shell resides evenly spread on its outer surface.

In this case the outer surfaces are the outer surfaces of the end plates. While charges can't leave individual plates, the fields that they produce can induce charge separation on the plates around them. So what 'migrates' to the outer surfaces is a net induced charge.

When you look at a collection of charges from a far enough distance such that the separation between the individual charge groups becomes negligible when compared to that distance, the net field becomes indistinguishable from a single net charge. Since we're looking at large parallel plates, then from a distance it should look like a single plate carrying the net charge. So we expect that the field will be uniform and of equal magnitude on both sides of the structure. That implies equal surface charge on the outer surfaces, so half the net charge on each.

16. Jan 10, 2016

### gracy

whenever there is a system of some plates and none of the plates are earthed then both of the end plates would carry half of the total charge present in the system.
Right?
Is it applicable for system of any number of plates?

17. Jan 10, 2016

### cnh1995

Yes.You can verify it for 3 plates by the method I used in #14.

18. Jan 10, 2016

### gracy

So if there is a system of plates (actually a system of any number of plates)and no plate has been earthed then outer surfaces of both outer most plates will contain half of the totl charge in the system.And if any one of the plates is grounded then in that case outer surfaces of both outer most plates will have zero charge.
Right?
And what if more than one plate is grounded?

19. Jan 11, 2016

### cnh1995

Right.
Then also, outer surface of the outermost plates have 0 charge. If any one plate is grounded, that means the net charge in the system is 0.

Last edited: Jan 11, 2016