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

[gneill]

Then why no charge transfer occur from Earth as charge are transferred from Earth if there is potential difference between earthed plate and the other plate(s)?

If you are referring to the example where one outer plate is connected to +V and the other to -V, and the middle plate is connected to the ground reference, then the net required charge on the middle plate is zero. Hence no charge moves onto or off of the middle plate.

 

[gracy]

then the net required charge on the middle plate is zero.

What does required charge mean?

 

[gracy]

According to @cnh1995

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

And there is potential difference between earthed plate and other plate(s) then why no charge transfer occur from Earth to plate b as charge are transferred from Earth if there is potential difference between earthed plate and the other plate(s)?

 

[cnh1995]

According to @cnh1995
And there is potential difference between earthed plate and other plate(s) then why no charge transfer occur from Earth to plate b as charge are transferred from Earth if there is potential difference between earthed plate and the other plate(s)?

That will depend also on where the other end of the middle plate is connected. Here, it is connected in between +ve terminal of one battery and -ve terminal of the other battery. Both batteries have same voltage V. Hence, charge formation on the plate is avoided. I've mentioned it in #89.

 

[gracy]

How to figure out that there is potential difference between earthed plate and other plate(s) or not?

 

[gneill]

What does required charge mean?

The total charge required to establish the electric fields between the plates. When the circuit is at steady state (equilibrium), the potential difference across a pair of plates matches the potential difference applied externally (by the voltage source). When the potentials match, charge stops moving. The required charge is the charge needed to establish equilibrium.

I provided a drawing previously where the electric field lines were shown.

 

[cnh1995]

That will depend also on where the other end of the middle plate is connected. Here, it is connected in between +ve terminal of one battery and -ve terminal of the other battery. Both batteries have same voltage V. Hence, charge formation on the plate is avoided. I've mentioned it in #89.

If the two voltages were different, there would be some charge "needed" on the middle plate to establish electrostatic balance.

 

[gneill]

How to figure out that there is potential difference between earthed plate and other plate(s) or not?

Look for batteries or current sources in the external circuit. The external circuitry establishes the potential differences.

 

[gracy]

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

Why?
Isn't this possible

Why middle plate can not have negative charge equal to positive charge present on plate a or plate c?(Arrow should be reversed ;electric field does not start with negative charge)

 

[cnh1995]

Why?
Isn't this possible
View attachment 92793
Why middle plate can not have negative charge equal to positive charge present on plate a or plate c?(Arrow should be reversed ;electric field does not start with negative charge)

Plate B is shared by the two capacitors. Hence, charge on plate B must be equal(and opposite)to the sum of the charges on plate A and plate C.

 

[cnh1995]

Why middle plate can not have negative charge equal to positive charge present on plate a or plate c?

Plates 1 and 4 have charge +Q each, plates 2 and 3 have charge -Q each. But plate B is formed by 2 and 3 together. Hence, it will have total charge of -2Q.

 

[gneill]

Why?
Isn't this possible
View attachment 92793
Why middle plate can not have negative charge equal to positive charge present on plate a or plate c?(Arrow should be reversed ;electric field does not start with negative charge)

A couple of reasons.

1. There can be no electric field inside a conductor, so the field lines from the right plate could not reach the charges if they were located on the left side of the middle plate. They can't be in the middle of the plate for the same reason. The charges are pulled to the outsides of the middle plate by the positive plates on either side.

2. The current flowing into a component must equal the current flowing out of the component. For a capacitor, if some charge Q is pushed onto one plate then the same amount of charge Q must be removed from its opposite plate in the capacitor. If a plate happens to be shared by two capacitors the rule applies to both of them separately; The net charge on that shared plate is then the sum of the charges required to satisfy both separate requirements.

The bottom line is that charges on the plates of a capacitor sit at the inside surfaces that face each other and these surfaces will have equal charges of opposite sign. If a single plate has faces used as plates in different capacitors then the rules apply to each pair of facing plates separately as though they are entirely separate capacitors. If we want to we can sum up the total charges and arrive at a net charge for the plate.

In order for charges to move onto or off of a plate there must be an external connection and a circuit. Otherwise charges won't move. Connecting one lead of a capacitor to a battery will not cause charge to flow onto the one plate.

 

[gracy]

So ,we have Q=CV=$\frac{ε0A}{d}$V
So,net charge on plate A is $\frac{ε0A}{d}$V
Similarly net charge on plate C is $\frac{ε0A}{d}$V
Net charge on plate B is equal to sum of charges on faces 2 and and 3 which is equal to - $\frac{2ε0A}{d}$V
Right?

 

[gneill]

Yes, that looks good!

 

[gracy]

Thank you so much @gneill you are the best.