Nonconducting Rod bent into Circle

1. Mar 26, 2013

Soccerdude

Question

A thin nonconducting rod with a uniform charge distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at (a) z = 0 (b) z = ∞ (c) In terms of R, at what postive value of z is that magnitude maximum? (d) If R = 2.00 cm and Q = 4.00 μC, what is the maximum magnitude?

Relevant Equations

dE = (kedq/r2)$\hat{r}$
λ = Q/Length

Solution Attempt

I'm not really sure how to even approach this problem. I know that E = kzQ/(z2+R2)3/2 but i'm not quite sure how to reach this.

Help is much appreciated.

2. Mar 26, 2013

tms

Part (a) you should be able to figure out by inspection, from symmetry considerations.

For part (b), consider an arbitrary point on the z-axis, and find an expression for the field due to an infinitesimal charge element on the circle. Then integrate. Again, keep symmetry in mind.