Nonconducting Rod bent into Circle

[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 positive 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 = (k_edq/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.

 

[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.