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F = del(p.E) and F = (p.del)E are equivalent

  1. Nov 13, 2013 #1
    Question: In the electrostatic case, the expressions F = del(p.E) and F = (p.del)E are equivalent:

    I am having trouble with how to show they are equivalent

    In the second equation, I expanded it out to give F= px (dE/dx) + py (dE/dy) + pz(dE/dz)

    Any help as to how to do this would be much appreciated

    thanks
     
  2. jcsd
  3. Nov 13, 2013 #2

    Meir Achuz

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    You have to use the vector differential operator equation
    [tex]\nabla({\bf p\cdot E)=p\times(\nabla\times E)+(p\cdot\nabla)E}[/tex],
    and curl E=0.
     
    Last edited: Nov 13, 2013
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