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

[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.