A thin non-conducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R (Figure). 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 = ∞?

(c) In terms of R, at what positive value of z is that magnitude maximum? 

(d) If R = 2.00 cm and Q = 4.00μC, what is the maximum magnitude?

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R.