Electric Field of a Uniformly Charged Ring

[ILoveCollege]

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.

Homework Equations

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?

 

[Maxim Zh]

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).

 

[ILoveCollege]

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?

 

[Maxim Zh]

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

<br /> \begin{array}{l}<br /> r = 8.1 \text{cm}; \\<br /> 0 &lt; \phi &lt; 2\pi; \\<br /> z = 0.<br /> \end{array}<br />

Since the ring is charged uniformly there is no need to calculte the integral explicitly.
Just derive the E_z 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.