Halliday, Resnick & Walker — Electric Fields: Problem 6

6 A thin nonconducting rod with a uniform distribution of positive charge \( Q \) is bent into a complete circle of radius \( R \) (Fig. 22-22). 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) \( z = 0 \) and (b) \( z = \infty \)? (c) In terms of \( R \), at what positive value of \( z \) is that magnitude maximum? (d) If \( R = 2.00 \text{ cm} \) and \( Q = 5.00 \text{ }\mu\text{C} \), what is the maximum magnitude?