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Dipole moment of polarized sphere

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a polarised sphere of radius R the polarization is given by
    P vector = (ar^2 + b) r hat = ( ar+ b/r) r vector
    Where a and b are constant


    2. Relevant equations

    Find the dipole moment of the sphere

    3. The attempt at a solution

    I knew that P (polarized)= delta p / delta volume
    So to find dipole moment
    I'll take : delta p = [itex]\int p . dv[/itex]
    I have a solution manual written in it that
    P.r vector = Q
    So the delta p = Q/4 pi r^2
    How they got this equ.
    Should i use the polarized equ. That given
    Im so confused

    Help
     
    Last edited: Dec 4, 2012
  2. jcsd
  3. Dec 3, 2012 #2
    Is here anyone can help!,,
     
  4. Dec 4, 2012 #3

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I don't think you need to do any calculation here.

    Note that the polarization vector P has a direction that is radially outward at each point of the sphere and the magnitude of P depends only on r.

    So, if you consider a small element of volume dV1 at some point in the sphere at a distance r from the center, the dipole moment of that element will be dp1 = P1dV1.

    Now consider a second volume element dV2 (same size as dV1) that is at the same distance r from the center but is on the opposite side of the center from dV1. The dipole moment of that element will be dp2 = P2dV2.

    How do the magnitudes of dp1 and dp2 compare? How do their directions compare?

    What would you get if you add them: dp1 + dp2 = ?
     
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