Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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.

    Attached Files:

    Last edited: Dec 27, 2012
  4. Dec 28, 2012 #3
    Thanks , I can see that in Cartesian coordinates .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook