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 2ik$E_{0}$^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