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Nonconducting Rod bent into Circle

  1. Mar 26, 2013 #1
    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)[itex]\hat{r}[/itex]
    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. jcsd
  3. Mar 26, 2013 #2

    tms

    User Avatar

    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.
     
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