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Feynman lectures electric dipole question

  1. Jul 2, 2015 #1
    For some reason, I'm having trouble with what I feel should be a relatively simple derivative to take. Feynman is differentiating the potential to find the z-component of the electric field. He has:
    [tex]-\frac{\partial \phi}{\partial z} = - \frac{p}{4 \pi \epsilon_0} \frac{\partial }{\partial z} \left(\frac{z}{r^3}\right) = -\frac{p}{4 \pi \epsilon_0} \left(\frac{1}{r^3} - \frac{3z^2}{r^5} \right )[/tex]

    I'm not quite sure how he takes that derivative.
     
  2. jcsd
  3. Jul 2, 2015 #2

    jasonRF

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    Science Advisor
    Gold Member

    Note that ## r = \sqrt{x^2 + y^2 + z^2} ##. So insert ## \sqrt{x^2 + y^2 + z^2} ## everywhere you see a ## r ##, take the derivative, and then
    rewrite powers of ##x^2 + y^2 + z^2## in terms of ##r##. Does that help?

    jason
     
  4. Jul 2, 2015 #3

    jtbell

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    Staff: Mentor

    Or apply the chain rule in the initial derivative to get an expression that contains ##\partial r / \partial z##, then evaluate that derivative using ##r = \sqrt{x^2 + y^2 + z^2}##, and finally rewrite the result completely in terms of ##r##.
     
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