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Electric field at centre of hollow half sphere

  1. Jan 25, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-1-25_12-3-58.png

    2. Relevant equations


    3. The attempt at a solution
    I figured you could consider it as infinitely many rings? Here is what I did so far:
    upload_2017-1-25_12-4-55.png

    I feel like 0 is the wrong answer. Can anyone help me? Thanks.
     
  2. jcsd
  3. Jan 25, 2017 #2

    fresh_42

    Staff: Mentor

    For future posts: please try to type in your messages as it is difficult to impossible to read it on mobile devices.
     
  4. Jan 25, 2017 #3

    TSny

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    Gold Member

    Your notation is confusing. The axis of the rings is the z-axis, but you use the symbol ##x## to denote the position of the center of a ring. Also, you appear to initially use the symbol ##R## for the radius of a ring, but then later use ##R## for the radius of the hemisphere. (The problem statement says the radius of the hemisphere is ##a##.) Also, the symbol for the surface charge density as specified in the problem is ##\rho_s##.

    Nevertheless, your final integral looks correct except for the upper limit of integration. [Edit: Should your integration variable be ##\theta## or ##\phi## (if these symbols are defined according to the problem statement)?]
     
    Last edited: Jan 25, 2017
  5. Jan 25, 2017 #4

    cnh1995

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    Everything looks fine except the limits of your final integral. Are you sure Φ varies from 0 to 2π?
    Edit: TSny beat me to it while I was typing..
     
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