Electric Field of a Uniformly Charged Ring

  • #1

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?
 

Answers and Replies

  • #2
45
0
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).
 
  • #3
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?
 
  • #4
45
0
You need to integrate only over the charged area. In cylindrical coordinates it is

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

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.
 

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