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

[wobblybird]

Hi,

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

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

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

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

Thank you so much!

 

[UltrafastPED]

Hunt through the vector identities here: http://en.wikipedia.org/wiki/Vector_calculus_identities#Vector_dot_product

You want grad(a.b).

 

[Office_Shredder]

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