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Divergence in spherical coordinates.

  1. Aug 6, 2013 #1
    I want to verify:
    [tex]\vec A=\hat R \frac{k}{R^2}\;\hbox{ where k is a constant.}[/tex]
    [tex]\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial (R^2A_R)}{\partial R}+\frac{1}{R\sin\theta}\frac{\partial (A_{\theta}\sin\theta)}{\partial \theta}+\frac{1}{R\sin\theta}\frac{\partial A_{\phi}}{\partial \phi}[/tex]
    [tex]\Rightarrow\;\nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial \left(R^2\frac{k}{R^2}\right)}{\partial R}= \frac{1}{R^2}\frac{\partial k}{\partial R}=0[/tex]
     
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  3. Aug 6, 2013 #2

    HallsofIvy

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    Science Advisor

    I don't have any problem with that until the last part. What does [itex]\partial k/\partial R[/itex] mean? If "k" is the unit vector in the z direction, it is a constant, and any derivative of it is 0.
     
  4. Aug 6, 2013 #3
    He defines ##k## as a constant. So ##\frac{\partial k}{\partial R}## is the partial derivative of ##k## with respect to the variable ##R## which is zero, as he gets.
     
  5. Aug 6, 2013 #4
    Thanks, this is part of a problem in Electrodynamics where the solution manual claimed it is not zero. I just want to verify.

    Thanks for the help.
     
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