A ring that has radius a lies in the z = 0 plane with its center at the origin.

Question

A ring that has radius a lies in the z = 0 plane with its center at the origin. The ring is uniformly charged and has a total charge Q.
(a) Find Ez on the z axis at 0.1a.
________?______kQ
________?__________a2


(b) Find Ez on the z axis at 0.5a.
___________?______________kQ
___________?_______________a2


(c) Find Ez on the z axis at 0.8a.
___________?________________kQ
___________?_______________ a2


(d) Find Ez on the z axis at a.
___________?______________kQ
___________?_______________a2


(e) Find Ez on the z axis at 2.3a.
______________?_______________kQ
______________?_________________a2


(f) Use your results to plot Ez versus z for both positive and negative values of z. (Assume that these distances are exact. Do this on paper.)

Explanation / Answer

Ez = 2pkq(1-z/vz^2+a^2) Ez(0.1a) = kQ(0.1a)/(0.1a)^2+a^2)3/2 =0.098 kQ/a^2 Ez(0.5a) = kQ(0.5a)/(0.5a)^2+a^2)3/2 =0.357kQ/a^2 Ez(0.8a) = kQ(0.8a)/(0.8a)^2+a^2)3/2 =0.38kQ/a^2 Ez(a) = kQ(a)/(2a^2)3/2 =0.35kQ/a^2 Ez(2.3a) = kQ(2.3a)/(2.3a)^2+a^2)3/2 =0.14kQ/a^2

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