Charge Distribution in parrallel plate capacitor-I

For balance in any system, proper distribution of things are needed.

Proper distribution of the natural resources are needed to keep the balance in our ecosystem.

In a system of a car and a van ,proper weight distribution is needed to avoid accidents.

In a parallel plate capacitor the charges on plates get distributed to balance the total charge.

As the parallel plate capacitor is used mostly let’s look at the charge distribution thoroughly.

We have a parallel plate capacitor with plate named ‘A and ’B’ with charges +Q1 and +Q2 respectively.

Now to calculate electric field between the plates we took a point ‘P’ on the gaussian surface(dotted).

The electric field due to plate A would be E1 pointing towards plate A .

The electric field due to plate B would be E2 pointing towards plate B.

So there would be a non zero electric field due to different charges and the direction would be defined by the direction of the larger electric field.

Let’s see the flux through the gaussian surface.

The electric field inside the plate ‘A’ and ‘B’ is zero as the electric field inside a conductor is zero.

Lets the area vector be ‘a’ and the electric field at point ‘M’ and ‘N’ is always perpendicular to ’a’ vector.

The flux in through the gaussian surface inside the conductor is zero as the field is zero.

Again the flux through other two edges of the gaussian surface is zero .

So here the total flux through the gaussian surface is zero.

Now let's look in the charge distribution.

From the gauss's law the total flux through the gaussian surface is

Here the total flux is zero ,so the charge enclosed must be zero.

As the total enclosed charge is zero , the sum of Q1 and Q2 must be zero

The magnitude of the charges is same but the nature is opposite.

So if the charge on the plate is Q then the charge on the plate B would be -Q.

The net charge on the inner surface of the plates has to be zero.

Revision

The electric field inside conductor is zero. So the flux through the gaussian surface inside the conductor is also zero.

The area vector is perpendicular to the electric filed in the other two edges of the gaussian surface that's why the dot product of them ,flux is zero.

As the total flux is zero , so from the gaussian law the total enclosed charge is zero.

The charges on the inner surface of the plates are same in magnitude but opposite in sign.

The End