A total amount of positive charge Q is spread onto a nonconducting flat circular annulus of inner radius a and outer radius b. The charge is so distributed so that the charge density (charge per unit area) is given by , where r is the distance from the centre of the annulus to any point on it. We have to show that the potential at the centre of the annulus is given by

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Charge density inside the nonconducting flat circular annulus is

.

The total charge in the annulus is Q. Therefore, we have

And

.

By considering a ring of radius r concentric with the annulus and inside the annulus, and using the definition of electric potential we calculate the potential at the centre by integration

Substituting for k in V , we get