Role of ground in charging a parallel plate capacitor

[Tanya Sharma]

I am new with the topic Capacitors .I have read that a capacitor can be charged in two ways .One using the battery which I understand .The other is by charging one plate and grounding the other plate .I am not able to understand how this is done .

Suppose +q charge is given to a plate ,say A.This charge will uniformly distribute on the two surfaces each having charge q/2 .This charge +q/2 on the inner surface of A induces a charge -q/2 on the inner surface of the other plate ,say B .The outer surface of B will have charge +q/2 .When plate B is grounded , the potential of plate becomes equal to the potential of the ground ,.ie zero .Electrons flow from the ground neutrilising the outer surface charge of B .

I am not clear about few things

1) The above process should leave equal and opposite charges on the inner surfaces of the plates ,but +q/2 charge on the outer surface of A,thus leaving capacitor with a net positive charge .

2)Not clear about the role of ground .How this zero potential of ground is causing the electrons to flow between the ground and the outer surface of plate ,B .In order for the current to flow ,potential difference should exist .Potential of the ground is zero,but what is the potential of plate B?

 

[Jano L.]

Your description is fine until

,but +q/2 charge on the outer surface of A,thus leaving capacitor with a net positive charge .

If the capacitor still has some positive charge, it would attract negative charges from the ground, which plays the role of large reservoir of negative charges. This will stop only if the capacitor has zero field outside the plates - no force pulling the electrons from the ground.

The only way how the field outside can be zero is that both plates are charged with equal amount of charge of opposite sign. And because opposite charges attract, the charge will end up on the inner surfaces only.

 

[sophiecentaur]

When you 'charge' a capacitor by applying a PD across it you are adding charge to one plate and an equal and opposite charge to the other. It is a differential charge, in fact and the amount of charge will depend upon the Potential Difference across the plates. This PD is independent of whether or not one of the plates is connected to earth.
If you simply take a capacitor and connect one plate to a positive supply (with the negative supply terminal grounded perhaps) then the only capacitance involved will be the capacitance of a small cylinder of metal with respect to ground (perhaps 1pF?) Hence there will be a minuscule charge stored in the system. This charge is also a differential charge with the other charge being held on the Earth. (You don't get large amounts of isolated charge anywhere as the total net charge in the Universe will be zero)

When you refer to "charging one plate", how is this to be achieved? If you bring a charged object up to the plate then this object will have been charged in some way, which involved giving the charges some potential energy (Power supply, rubbing etc) and will be storing that charge by virtue of its capacitance relative to the original charging system (ground, normally).

The same principle applies to the two cases but 'charging objects' normally involves much less actual charge than what can be stored between the plates of a capacitor, which has been designed to have a very much larger capacitance.

 

[ehild]

I am new with the topic Capacitors .I have read that a capacitor can be charged in two ways .One using the battery which I understand .The other is by charging one plate and grounding the other plate .I am not able to understand how this is done .

Suppose +q charge is given to a plate ,say A.This charge will uniformly distribute on the two surfaces each having charge q/2 .

That happens for an isolated charged plate. The charges repel each other and move away from each other as far as possible. The charge of the metal plate appears as surface charge on both sides.

This charge +q/2 on the inner surface of A induces a charge -q/2 on the inner surface of the other plate ,say B .The outer surface of B will have charge +q/2 .When plate B is grounded , the potential of plate becomes equal to the potential of the ground ,.ie zero .Electrons flow from the ground neutralising the outer surface charge of B .

I am not clear about few things

1) The above process should leave equal and opposite charges on the inner surfaces of the plates ,but +q/2 charge on the outer surface of A,thus leaving capacitor with a net positive charge .

Well, you can think that the inner q/2 charge is neutralised by the induced charge on the other plate. The outer charges still repel each other, and now half of them can go the the other side again. That will induce opposite charges on the inner side of the grounded plate, neutralizing the newly arrived q/4 charge and allowing the migration of other charges to the inner plate again. That goes on till all the original charge appears on the inner surface of the plate, and equal amount of opposite charge on the inner surface of the grounded plate.

2)Not clear about the role of ground .How this zero potential of ground is causing the electrons to flow between the ground and the outer surface of plate ,B .In order for the current to flow ,potential difference should exist .Potential of the ground is zero,but what is the potential of plate B?

The ground, the Earth serves as a very big conductor, infinite reservoir of charges.
First, when you charge a plate, it gets some potential with respect to infinity. You can consider the ground and infinity at the same potential.
There is an electric field around the charged plate and the other plate is at some potential with respect to the ground. When you connect it to the ground with a vire, there is a potential difference between the ends of the connecting wire, and electrons flow over till equilibrium is set up.

ehild

 

[Tanya Sharma]

Thanks everybody for the response...

The outer charges still repel each other, and now half of them can go the the other side again. That will induce opposite charges on the inner side of the grounded plate, neutralizing the newly arrived q/4 charge and allowing the migration of other charges to the inner plate again.

I didnt understand this...After +q/2 charge appears on plate A and -q/2 appears on plate B ,both A and B have +q/2 charge on their outer surfaces.

First, when you charge a plate, it gets some potential with respect to infinity.

But the plate B is electrically neutral having -q/2 charge on its inner and +q/2 charge on its outer surface .We know the potential difference between the plates ,but what is the potential of plate B with respect to infinity?