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Monopole Moment of a sphere of charge

  1. Feb 15, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm really bad at these type of problems. I'm supposed to find the monopole moment of this continuous charge distribution. its charge is

    [tex]\sigma = const*cos(\theta) [/tex]

    2. Relevant equations

    [tex]p = \int r'\rho(r')d\tau[/tex]
    which then since we are doing a surface charge should be
    [tex]p = \int r' \sigma da[/tex]

    3. The attempt at a solution
    Well, I want to do the double integral of something to find the charge distribution so I can find the monopole moment. I'm thinking something like
    [tex]p = \int_{0}^{2 \pi}\int_{0}^{2 \pi} r' * c \cdot cos(\theta) sin( \theta) r^2 d\phi d\theta[/tex]
    and I'm thinking that r' is just r so then it would be

    [tex]p = \int_0^{2\pi} d\phi \int_0^{\pi} r'^3cose(\theta)sin(\theta)d\theta[/tex]
    Last edited: Feb 15, 2008
  2. jcsd
  3. Feb 15, 2008 #2
    The obvious problem that then comes up is that then appears is that I get a 0 term from the second integral that makes my whole monopole moment zero. Is this correct?
  4. Feb 15, 2008 #3
    if you are supposed to calculate the monopole moment then you integrate the charge density only. the formulas you have above are those for a dipole moment. monopole moment is just total charge
  5. Feb 15, 2008 #4


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    The monopole moment is zero. Some of your formulas are wrong, as Capt. pointed out.
  6. Feb 15, 2008 #5
    Ok, thanks! I think I see what I did wrong!
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