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I Vector integration by parts

  1. May 18, 2016 #1
    Screen Shot 2016-05-18 at 2.57.39 PM.png

    I was trying to derive the following results from 4B.8 as suggested by using the vector triple product identity but have been unsuccessful in deriving ##\vec{L_R}## and ##\vec{S_R}## in the end. After using the identity and finding the integrand to be ## \vec{E}(\vec{r}\cdot\vec{B}) - \vec{B} (\vec{r} \cdot \vec{E}) ## what would be the next best step to take to re-derive the 4B.10 and 4B.11?
  2. jcsd
  3. May 18, 2016 #2


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    Staff: Mentor

    I haven't tried it, but my guess is that this is not the right identity to use, and that you should rather use the Jacobi identity that is a couple of lines below in the Wikipedia page.
  4. May 18, 2016 #3
    Okay. I've looked into that identity as well now, and after using it, still don't quite get any further since it reduces back to the case of the integrand equalling ## \vec{E}(\vec{r}\cdot\vec{B}) - \vec{B} (\vec{r} \cdot \vec{E}) ##.
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