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Doubt regarding derivation of bound charges in dielectric

  1. Dec 27, 2012 #1
    In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9)
    {Here the potential at r is calculated due to the dipole at r' )

    V(r) = ∫[itex]\frac{x.P(r')}{X^2}[/itex]d[itex]\tau'[/itex]

    Here X = r - r' , and x = unit vector in the direction of X

    Then it is written that [itex]\frac{x}{X^2}[/itex] = [itex]\nabla'[/itex](1/X).

    since X = (r-r') , and ∇' = (∂/∂r')[itex]\widehat{r'}[/itex] ...

    Shouldn't ∇'(1/X) be (1/X^2)[itex]\widehat{r'}[/itex] ?
     
    Last edited: Dec 27, 2012
  2. jcsd
  3. Dec 27, 2012 #2

    TSny

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    It might be best to work it out in Cartesian coordinates where all coordinates are written explicitly. See if you can fill in the details of the derivation outlined in the figure.
     

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    Last edited: Dec 27, 2012
  4. Dec 28, 2012 #3
    Thanks , I can see that in Cartesian coordinates .
     
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