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Electric field at centre of a hollow hemisphere shell.

  1. Jan 21, 2017 #1
    1. The problem statement, all variables and given/known data
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    2. Relevant equations
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    N5fF11a.png '



    3. The attempt at a solution

    Please excuse the poor writing. I believe it should be legible enough, but if you have any questions, i'll clarify or rewrite it.

    RdtZpbc.png

    Please excuse the poor writing. I believe it should be legible enough, but if you have any questions, i'll clarify or rewrite it.

    My steps for solving this was filling in the values into the formula given. Using a square differential element on the surface of the sphere, as well as spherical co-ordinates.

    i'm sure i just have a small error somewhere in the math, but i'm not too sure where... i've redone the question 3 times.




    These two sources, among others, show that my answer is wrong. Though I did my question differently, so i cant be sure where i went wrong.



    http://www.personal.utulsa.edu/~alexei-grigoriev/index_files/Homework2_solutions.pdf
     
  2. jcsd
  3. Jan 21, 2017 #2

    TSny

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    Welcome to PF!

    Looks like you treated the unit vector ##\hat{r}## as a constant vector when you pulled it out of the double integral. Does the direction of ##\hat{r}## vary as you integrate over the surface? If so, you cannot treat it as a constant vector.
     
  4. Jan 22, 2017 #3
    How would I treat the vector? My apologies. Calculus is not my strong suit.
     
  5. Jan 22, 2017 #4
    How would I go about doing that? Calculus is not my stop suit. And also, thanks for the help.
     
  6. Jan 22, 2017 #5

    TSny

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    Use symmetry to see which direction the net E field will point. Then just work with the component of E that is in that direction. (Project your integrand into that direction.)
     
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