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Electric field due to a distributed charge over a ring

  1. Apr 4, 2015 #1
    1. The problem statement, all variables and given/known data
    .A ring-shaped conductor with radius a = 0.025 m has a total positive charge Q = 0.125 x 10-9C uniformly distributed around it. The center of the ring is at the origin of coordinates O.

    What is the electric field (magnitude and direction) at point , which is on the x-axis at x = 0.4m.

    2. Relevant equations
    dq = λ(ds)
    Q = λ(2πr)
    dE = ((k)(dq)/r2) * (r^)

    3. The attempt at a solution
    So I figured out how to solve the electric field using the equations above, but for some reason I am not getting 0 for the electric field in the y-direction. I know that it has to be zero because all the electric fields cancel out in the vertical direction so I'm assuming my value for r^ is incorrect. Is it supposed to be (0.4i^ + 0.025j^)/(r)? It seems like it should be ((0.4i^ + 0j^)/(r) in order to get 0 for the vertical direction. After solving I end up with E = (6.98i^ + 0.4364j^) and the electric field in the x-direction is correct, but I don't think there is supposed to be a field in the y-direction. So, can someone tell me if my value for r^ is correct?
     
  2. jcsd
  3. Apr 4, 2015 #2

    TSny

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    By drawing a figure you should see that ##\hat{r}## will have y and z components that vary as you integrate over the ring.
     
    Last edited: Apr 4, 2015
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