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Dipole moment of non-conducting spherical shell

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm trying to find the dipole moment of

    The surface charge distribution is:

    [tex]
    \sigma = \sigma_{0} sin 2 \theta
    [/tex]

    2. Relevant equations



    3. The attempt at a solution

    [tex]
    p_z=\int_{0}^{\pi}{\sigma* z* dA } = \int_{0}^{\pi}{(\sigma_0 \sin{2 \theta})*(acos{\theta})*(2\pi a^2 \sin{\theta}d\theta)}
    [/tex]

    Doing so I obtain

    [tex]
    ( \sigma_{0} a^3 \pi^2)/(2)

    [/tex]

    Can that be the answer?
     
  2. jcsd
  3. Oct 14, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    You should also explicitly show (or give a good argument for why) [itex]p_x=p_y=0[/itex] and then write your final answer in vector form (since dipole moment is a vector!) as [itex]\textbf{p}=\frac{\sigma_{0} a^3 \pi^2}{2}\mathbf{\hat{z}}[/itex], but other than that it looks good to me!:approve:
     
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