# Electric Field of a Uniformly Charged Ring

## Homework Statement

A uniformly charged ring of radius 8.1 cm has a total charge of 118 micro Coulombs. The value of the Coulomb constant is 8.98755e9 N M^2/C^2. Find the magnitude of the electric field on the axis of the ring at 1.15 cm from the center of the ring. Answer in units of N/C.

F= k Qq/ r^2
E= kq/r^2

## The Attempt at a Solution

I tried subtracting 1.15 cm from 8.1 cm for "r" and plugged that "r" value in the F equation but that answer is wrong. By axis , do they mean horizontally (as in along the diameter) or vertically?

The ring axis is vertical (normal to the diameter).

You should sum the fields produced by each part of the ring (it's an integral over the ring).

Why would I need to integrate? It already gives me the total charge for the ring. from what points would I integrate? 0 to 8.1?

You need to integrate only over the charged area. In cylindrical coordinates it is

$$\begin{array}{l} r = 8.1 \text{cm}; \\ 0 < \phi < 2\pi; \\ z = 0. \end{array}$$

Since the ring is charged uniformly there is no need to calculte the integral explicitly.
Just derive the Ez component of the field produced by a point charge placed on the ring. Than multiple it by the factor determined by the linear charge density of the ring.