Question

A uniformly charge ring with radius R and having line charge density λ kept in xy plane

with its centre at origin. Find electric field intensity E, for this ring at a height L on z axis.

Answer 1

We see that

$$r^2=L^2+R^2,\\\space\\ \cos\theta=L/r=L/\sqrt{L^2+R^2}.$$

Determine the electric field intensity:

$$\text dE_z=k·\text dq/r^2\cos\theta=\frac{kx\text dq}{(L^2+R^2)^{3/2}}.\\\space\\ E_z=\int \frac{kx\text dq}{(L^2+R^2)^{3/2}}=\frac{2\pi k\lambda RL}{(L^2+R^2)^{3/2}}.$$