What is the Electric Field at a Small Distance from a Charged Ring?

[thepopasmurf]

Homework Statement

I have a ring, radius a, with a charge distributed evenly around it. Using a gaussian cylinder of radius r, r<<a (or otherwise). Find the electric field at at small distance r away from the centre of the ring, r is in the plane of the ring.

I know that the answer is

$$\frac{Qr}{8\pi\epsilon_0 a^3}$$

Homework Equations

$$\int E\cdot ds = Q/\epsilon_0$$

The Attempt at a Solution

I can't get started since I find that the charge enclosed is 0

Thanks

 

[Doc Al]

Don't try to use Gauss's law. (What would be your Gaussian surface? Is the field uniform across it?) Instead, integrate the field contributions from each part of the ring. (It might prove easier to work with the potential instead of the field.)