so we have the identity
\nabla\times\nabla\phi = 0
and from Maxwell's equations we have
\nabla\times \textbf{E} = -\frac{d\textbf{B}}{dt}
But we also have that
\textbf{E} = -\nabla\phi
So the problem I'm having is this
-\textbf{E} = \nabla\phi
which i substitute into the...
lets just go from basics, step by step, assuming everything is complex
(sigma E)* . E
where E(vector) and sigma(scalar) are complex
(sigma)* E* . E = sigma* |E|^2
or
sigma* (Ex*, Ey*, Ez*).(Ex, Ey, Ez) = sigma* [|Ex|^2+|Ey|^2+|Ez|^2] = sigma* |E|^2
must take modulus of the field...