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How to integrate the electric field of the square sheet

  1. Dec 18, 2016 #1
    • ✱✱ members are reminded that homework help requests must use the 3-header template provided ✱✱
    Sorry
    i have one question to ask

    how to integrate the electric field of the square sheet( see the pink circle below)
    it looks hard for me

    thank you very much
     

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  2. jcsd
  3. Dec 18, 2016 #2

    blue_leaf77

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    Hint: Try substitution method ##2u+z^2=t##. You might still need one more substitution, but I will not comment any further before you show your own work.
     
  4. Dec 18, 2016 #3

    cnh1995

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    Use the substitution
    √(2u+z2)=t.
     
  5. Dec 18, 2016 #4

    blue_leaf77

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    Yes you can also do that, and may be in the third line you can use the fact that the derivative of ##\sec x## is ##\sec x \tan x##. But your way is kind of longer than necessary.
     
  6. Dec 18, 2016 #5
    Did i make mistake in my calculation?
     

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  7. Dec 18, 2016 #6

    blue_leaf77

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    Looks good. Now you only need to do the last integral and change back to the original variable ##u## and plug in the integral limits.
     
  8. Dec 18, 2016 #7

    cnh1995

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    If you use this substitution,
    du/√(2u+z2) can be replaced by 'dt' and u+z2=(t2+z2)/2.
    So, you'll simply get it as ∫2dt/(t2+z2) which is (2/z)tan-1(t/z).
    You get your answer in just two steps.
     
  9. Dec 18, 2016 #8
    Oh i see thank you
     
  10. Dec 18, 2016 #9
    i dont know why i do it wrong (is there a minus sign??)
    can you help me to check it
    thank
     

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  11. Dec 18, 2016 #10

    blue_leaf77

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    I missed one mistake in your work in post #5. In the last line, you should have removed the integral and the integration element. There should only be #\theta## there.
    I don't know why you are redoing your work, you are almost there in post #5.
     
  12. Dec 18, 2016 #11
    i redo my work by other way

    and i found the answer looks different from my answer in post 5(which i successfully do it)
    something looks crazy when the answer in my last post looks totally different.
    but i cannot find any mistake
     
  13. Dec 18, 2016 #12
    yes

    i should remove in the integral but i always forget

    thank you
     
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