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Electric field at center of charged hemispherical shell

  1. Nov 1, 2015 #1

    Titan97

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    Gold Member

    1. The problem statement, all variables and given/known data
    Find Electric field at center of charged hemispherical shell

    2. Relevant equations
    In spherical coordinates, $$dA=R^2\sin\phi d\phi d\theta$$

    3. The attempt at a solution
    Untitled.png
    From the image, Enet=2dEy=2dEcosφ
    $$dE=\frac{kdq}{R^2}E$$
    $$dE=\frac{k\sigma dA}{R^2}$$
    $$dE=\frac{k\sigma R^2\sin\phi d\phi d\theta }{R^2}$$
    $$dE_{total}=2k\sigma\sin\phi\cos\phi d\phi d\theta$$
    $$E=\int_0^{2\pi}\int_0^{\frac{\pi}{2}}2k\sigma\sin\phi\cos\phi d\phi d\theta$$
    $$E=\frac{\sigma}{2\epsilon_0}$$
    But given answer is $$E=\frac{\sigma}{4\epsilon_0}$$
     
  2. jcsd
  3. Nov 1, 2015 #2

    blue_leaf77

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    Homework Helper

    The integration over the azimuthal angle from 0 to ##2\pi## already takes the factor of two in your expression ##dE_{total}=2k\sigma\sin\phi\cos\phi d\phi d\theta## into account. So you should have removed it from ##dE_{total}##.
     
  4. Nov 1, 2015 #3

    Titan97

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    Gold Member

    Thank you.
     
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