What is the Charge on a Capacitor with Given Area and Plate Separation?

[jbriggs444]

A plate can be "neutral" in the sense of having no excess charge but not be "neutral" in the sense of being at zero potential compared to some arbitrary reference.

A plate can be "non-neutral" in the sense of having excess charge but still be "neutral" in the sense of being at zero potential compared to some arbitrary reference (such as an earth).

 

[gracy]

If there is an external connections to plates then it is impossible that plates would be neutral?

 

[gneill]

A plate can be "neutral" in the sense of having no excess charge but not be "neutral" in the sense of being at zero potential compared to some arbitrary reference.

A plate can be "non-neutral" in the sense of having excess charge but still be "neutral" in the sense of being at zero potential compared to some arbitrary reference (such as an earth).

While that is all true, I'm not sure that introducing that distinction at this juncture is going to help Gracy with the immediate details that she needs to clear up. Perhaps it can be addressed as a new topic later?

 

[gneill]

If there is an external connections to plates then it is impossible that plates would be neutral?

That would depend upon whether or not the connects lead to something that will cause charge to flow (impose potential differences). Even so it is possible to arrange things so that the net excess charge will be zero! Here's an example:

The middle plate is externally connected (to ground), but is situated between two plates that have opposite potentials with respect to ground reference. The net result will be no excess charge on the middle plate, although it will have equal and opposite charges on its surfaces.

 

[gracy]

The net result will be no excess charge on the middle plate,

But plate A and C have plus charges,right?

 

[cnh1995]

That would depend upon whether or not the connects lead to something that will cause charge to flow (impose potential differences). Even so it is possible to arrange things so that the net excess charge will be zero! Here's an example:

View attachment 92776
The middle plate is externally connected (to ground), but is situated between two plates that have opposite potentials with respect to ground reference. The net result will be no excess charge on the middle plate, although it will have equal and opposite charges on its surfaces.

Seeing this diagram,can I say there won't be net charge on any plate because there isn't any 'closed electrical path "through" the dielectric'?

 

[gneill]

But plate A and C have plus charges,right?

No, one will be plus, the other minus. Look at the polarities of the two batteries. One establishes plate a at +V potential with respect to ground, the other establishes plate c at -V potential with respect to ground.

 

[cnh1995]

No, one will be plus, the other minus. Look at the polarities of the two batteries. One establishes plate a at +V potential with respect to ground, the other establishes plate c at -V potential with respect to ground.

Yeah..right..

 

[gneill]

Seeing this diagram,can I say there won't be net charge on any plate because there isn't any 'closed electrical path "through" the dielectric'?

No, the electric fields between the plates established by the potential differences suffices to influence charge movement in the plates and wiring. Remove the central plate from the scenario and you have a typical capacitor with a potential difference of 2V across it.

 

[cnh1995]

No, the electric fields between the plates established by the potential differences suffices to influence charge movement in the plates and wiring. Remove the central plate from the scenario and you have a typical capacitor with a potential difference of 2V across it.

So can I conclude plates A and C form a capacitor with space between them as dielectric and middle metal plate is just "polarized" because of the the electric field of the two plates.

 

[gracy]

pect to ground reference. The net result will be no excess charge on the middle plate, although it will have equal and opposite charges on its surfaces.

Plate b would have negative charges on it because of plate a and would have positive charges on it because of plate c,right?

 

[gneill]

So can I conclude plates A and C form a capacitor with space between them as dielectric and middle metal plate is just "polarized" because of the the electric field of the two plates.

Effectively yes, but note that the gaps between the middle plate and the outer ones are much smaller than the gap between the two outer plates. So the "new" capacitors thus formed will have higher capacitance than the two outer plates alone would have (recall the formula for capacitance of a parallel plate capacitor).

 

[cnh1995]

Effectively yes, but note that the gaps between the middle plate and the outer ones are much smaller than the gap between the two outer plates. So the "new" capacitors thus formed will have higher capacitance than the two outer plates alone would have (recall the formula for capacitance of a parallel plate capacitor).

Right.

 

[gracy]

In my OP i.e picture in #28
plate B would have negative charges on both the side as it's adjacent plates are having positive charges,where will positive charges of plate B go as initially plate B was neutral ?I think all the positive charges of plate B would go to Earth and plate B would have net negative charge.

 

[cnh1995]

In my OP i.e picture in #28
plate B would have negative charges on both the side as it's adjacent plates are having positive charges,where will positive charges of plate B go as initially plate B was neutral ?I think all the positive charges of plate B would go to Earth and plate B would have net negative charge.

Correct.

 

[gracy]

Plate A and C would have net positive charge,right?

 

[cnh1995]

Plate A and C would have net positive charge,right?

Yes. The middle plate alone will have -ve charge whose magnitude will be twice the +ve charge on each plate.

 

[gracy]

The middle plate is externally connected (to ground), but is situated between two plates that have opposite potentials with respect to ground reference. The net result will be no excess charge on the middle plate, although it will have equal and opposite charges on its surfaces.

I did not understand.Why can not Earth take or give any charges to plate b?

 

[gneill]

Plate b would have negative charges on it because of plate a and would have positive charges on it because of plate c,right?

Right. Sometimes it helps to sketch in the electric field lines that are imposed by the potential differences, and recall that electric field lines always begin on a positive charge and end on a negative charge.

 

[gracy]

The middle plate alone will have -ve charge whose magnitude will be twice the +ve charge on each plate.

Because Earth can give as much plate needs.

 

[gneill]

I did not understand.Why can not Earth take or give any charges to plate b?

It can. But it doesn't in this case. The situation calls for equal amounts of + and - charges on the middle plate, for a net sum of zero charge.

 

[gracy]

The situation calls for equal amounts of + and - charges on the middle plate, for a net sum of zero charge.

But Earth does not give them.Plate b already possesses that.

 

[cnh1995]

Because Earth can give as much plate needs.

That's one way to look at it.

If you look at this diagram, +ve terminal provides +Q charge to each plate, thus giving out total +2Q of charge. Hence, -ve terminal(ground) provides -2Q charge.

 

[gneill]

But Earth does not give them.Plate b already possesses that.

Correct.

 

[gracy]

Should not q transfer direction be other way around in #54?I am taking q to be electron because it is electron which actually travels.

 

[gracy]

How can we know this time Earth will give charges and at the other instance it won't?

 

[gneill]

Should not q transfer direction be other way around in #54?

How so? The batteries are driving charge in the direction that a current would flow.

 

[gracy]

I am taking q to be electron because it is electron which actually travels.

 

[gracy]

My bad that would be -q then not q,right?

 

[gneill]

How can we know this time Earth will give charges and the other it won't?

The charges are available if needed. If they are not needed, none are "borrowed".

 

[cnh1995]

How can we know this time Earth will give charges and the other it won't?

When there is a potential difference between earthed plate and other plate(s), Earth will give charge.

 

[gracy]

What is called " need" in this context?

 

[cnh1995]

What is called " need" in this context?

I believe its the potential difference.

 

[gneill]

I am taking q to be electron because it is electron which actually travels.

I've assumed conventional current, where charge carriers are assumed to be positive. It's less likely to confuse others if we stick to the convention.

 

[gracy]

When there is a potential difference between earthed plate and other plate(s), Earth will give charge.

And when Earth takes charge?