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Electric field at the center of a hemisphere

  1. Jan 23, 2017 #1
    1. The problem statement, all variables and given/known data

    What is the electric field at the center of a hemisphere bounded by r=a, 0<θ<pi/2 / and 0<∅< 2pi with a uniform surface charge density?
    2. Relevant equations
    (1/4piε0) p(r') ((r-r')/[r-r']^3) dr'
    3. The attempt at a solution
    Forgive my formatting
    ds= (r^2)sinθdθd∅ (In direction of r)
    p(r')=constant = σ
    r=r (in the direction of r)
    r'= 0 (I have trouble with understanding r and r')

    E= (σ/4piε0) ∫(0 to 2pi) ∫(0 to /2pi) (r^3)sinθdθd∅ / (r^3)
    E= (σ/4piε0) (2pi)(1)
    E= (σ/2ε0)

    Everywhere I look I see the answer to this problem is (σ/4ε0) and I cannot figure out where I am going wrong. I feel as though I am missing to include something in my equation but I am stumped, help would be appreciated.
     
  2. jcsd
  3. Jan 23, 2017 #2

    BvU

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    Gold Member

    I think you are missing the fact that ##\vec E## is a vector-- it has components (some of which are zero in your exercise)
     
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