Redistribution of charges in the concentric spherical shell - I

We know that liquid flow from a higher level to a lower level.

This flow of liquid happens due to the difference between the potential energies.

Analogous to liquids, the charge also flows from a higher potential to a lower potential.

The flow of charges in the conductor causes the redistribution of the charges.

Let's see the redistribution of charges on a concentric spherical shell

Suppose we have two concentric spherical shells connected by a conducting wire.

The radius of the inner spherical shell is and the radius of the outer spherical shell is .

The charge on the surface of the inner sphere is and that on the outer sphere is .

As the spheres are connected with a conducting wire the charge will flow from a higher potential to a lower potential through it.

The direction of flow of the charge will be decided by the potential difference between the two spheres.

Let's calculate the potential difference.

To calculate the potential difference, we have to know the potential on the surface of the inner and outer spheres.

The potential on the surface of the inner sphere due to the charge will be given by,

The charge on the outer shell will also contribute in the potential of inner shell.

Thus, the contribution in the potential of inner shell due the charge on the outer shell will be Given by

The net potential on the surface of the inner shell will be given by,

Further, writing the net potential on the surface of inner shell, we get

Similarly, the potential on the surface of the outer sphere due the charge on the outer sphere will be

And the contribution of the inner shell in the potential of the outer shell will be given by

Thus, the net potential on the surface of outer sphere will be given by,

Further, writing the potential on surface of the outer sphere, we get

The potential difference will be

Further proceeding for the potential difference we will get,

The redistribution of the charge is due to the flow of charges across the potential difference.

Let's talk about the direction of flow of the charges.

If the charge is positive the potential difference is greater than .

Means the inner shell is at higher potential and outer shell is at lower potential, and the charge will flow from inner shell to outer shell.

If the charge is negative, the potential difference is less than the .

Means the outer shell is at higher potential and inner shell is at lower potential and the charge will flow from outer shell to inner shell.

Revision

The potential difference is independent of the charge on the outer shell.

If the is positive, the potential difference is greater than the . The charge will flow from inner shell to outer shell.

If the is negative, the potential difference is less than the . The charge will flow from outer shell to inner shell.

The end