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Homework Help: Dipole approximation.

  1. Sep 2, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm reffering to http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dipole.html and the approximation [tex] r_1 - r_2 \approx = d \cos \theta[/tex]. I see that it is correct if I draw it up, but I wondered if there were any "more mathematical" ways to see this?

    Where does these kind of approximations come from? Is this just a special case or is it often used? I don't think I've seen this kind before.
     
  2. jcsd
  3. Sep 2, 2010 #2

    gabbagabbahey

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    The only approximation you need is that [itex]d \ll r [/itex], i.e. the dipole is very small compared to the distance(s) from its center at which you are interested in measuring the field or potential.

    To see how this approximation implies that [itex]|\textbf{r}_{+}-\textbf{r}_{-}|\approx d\cos\theta[/itex], you simply use the standard rules for vector addition/subtraction and calculate the magnitude of [itex]|\textbf{r}_{+}-\textbf{r}_{-}|[/itex], then Taylor expand it for small [itex]\frac{d}{r}[/itex].
     
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