Electrostatic shielding and capacitors

[Axe199]

First before asking the original question i need to make sure some of my concepts are correct:
1- what happens when a capacitor with its 2 plates having different areas is charged?
according to this forum https://van.physics.illinois.edu/qa/listing.php?id=23409 as the long as the difference in size does not extent the separation distance we can use an average of the areas or just the small one , but if the area of the big is much bigger than the distance of separation , eg: area ratio is 1:100 , then what happens to the extra electrons on the big plate ( given that the bigger plate will be the -ve one ) , will all the electrons concentrate around the area covered by the small positive plate ? or will it be spread all over the plate ?

 

[Simon Bridge]

OK let's makes this extreme.

A capacitor is just two conductors with some gap between them.

You could have a capacitor made of, say, an infinite conducting plane separated a small distance from an arbitrarily small conducting sphere (being the other "plate").

To charge the capacitor, you would move charges from one to the other (say from the plate to the sphere).

If they both started out neutral, the end result is that the sphere has the same, but opposite, charge as the plate.
It's just that the charge distributions are not the same.

So your questions:

what happens to the extra electrons on the big plate ( given that the bigger plate will be the -ve one ) ,

There are no "extra" charges on the big plate. Every charge lost by the big plate is gained by the small one.

... will all the electrons concentrate around the area covered by the small positive plate ? or will it be spread all over the plate ?

That is broadly correct - the charge distributions will no longer be uniform like in the ideal parallel-plate capacitor. Different geometries will produce different charge distributions.

In your example of unequal area parallel plates, the resulting distributions can be quite complicated because edge-effects can no longer be neglected.

You should probably also check your understanding of how electrostatic shielding works.

 

[Axe199]

when i said extra electrons i didn't mean "extra" from outside the system, i meant on the -ve plate , about the shielding , if you are referring to my title , i was going for another question then i changed my mind and forgot to change the title.
okay , about the question , so if we had a different setup , we have a large -ve charged plate, and a small grounded metal plate , we approach the small plate to the big plate , the small plate will be charged by induction , then we disconnect the ground, leaving 2 plates with different equal charges and distance between them filled with air , " kinda like a capacitor" , will the +ve charge induced on the small plate , force a new distribution on the larger plate?

 

[Simon Bridge]

when i said extra electrons i didn't mean "extra" from outside the system, i meant on the -ve plate , ...

OK then - the "extra" electrons on the -ve plate stay there.
What else would they do?

...about the shielding , if you are referring to my title , i was going for another question then i changed my mind and forgot to change the title.

Fair enough.

okay , about the question , so if we had a different setup , we have a large -ve charged plate, and a small grounded metal plate , we approach the small plate to the big plate , the small plate will be charged by induction , then we disconnect the ground, leaving 2 plates with different equal charges and distance between them filled with air , " kinda like a capacitor" , will the +ve charge induced on the small plate , force a new distribution on the larger plate?

This is not "kinda like a capacitor", it is a capacitor. As the charged and uncharged conductors approach each other, the charges on both conductors continuously rearrange to make sure the net field inside both the conductors are zero. There will be transients if the movement is rapid - you wanted the electrostatic description right?

 

[Axe199]

so the electrons will rearrange in each plate to cancel each others electric field, got it
what do you mean by electrostatic description?

 

[sophiecentaur]

so the electrons will rearrange in each plate to cancel each others electric field, got it
what do you mean by electrostatic description?

A better way of putting it might be to say they re-arrange themselves for minimal potential energy (same as water arranges itself at the bottom of an odd shaped bowl).

 

[Simon Bridge]

what do you mean by electrostatic description?

... as opposed to electro-dynamic.
While the charges are rearranging, there can be a non-zero electric field in a conductor.