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Gradient of the dot product of two vectors that are the same

  1. Sep 19, 2013 #1
    Hi,

    I am trying find the simplified expression of this:
    ∇(E [itex]\cdot[/itex] E)

    Where E is the electric field that can written as [itex]E_{0}[/itex](exp(i(kx-ωt))

    I know that since the two vectors are the same => E [itex]\cdot[/itex] E = [itex]||E||^{2}[/itex]

    Do I take the gradient of the magnitude then? It just doesn't feel right. Or should it be something like 2ik[itex]E_{0}[/itex]^2?

    Thank you so much!
     
  2. jcsd
  3. Sep 20, 2013 #2

    UltrafastPED

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  4. Sep 20, 2013 #3

    Office_Shredder

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    You can just take the gradient of the square of the magnitude - write it out as a function with no vectors involved, and calculate partial derivatives
     
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