- #1
capandbells
- 96
- 0
Homework Statement
I'm trying to figure out the heat dissipation in a volume V due to an incident harmonic electric field.
I know
[tex]
Q = \frac{1}{2}\int_V\mathrm{Re}\left(\mathbf{j}^{*} \cdot \mathbf{E}\right) d^3x
[/tex]
[tex]
= \frac{1}{2}\int_V\mathrm{Re}\left(\left(\sigma \mathbf{E}\right)^{*} \cdot \mathbf{E}\right) d^3x
[/tex]
My biggest problem is that I don't know how to evaluate that dot product. If someone could please either explain it or link me to a resource that explains working with complex vectors, I would appreciate it. I haven't taken an EM class yet and I've never had it explained elsewhere how to operate with complex vectors, so I am mostly flailing around with this stuff.