Finding time average Poynting vector

[kylie14]

Given E and H, obviously you can calculate Poynting vector (N=ExH), but then how do you find the time average of N (N')?

(I won't write all the question I'm trying to answer here but basically I'm trying the verify an equation, the says N' = 0.5* Re{ F x I* } where F and I are fields such that E= Re{F} and H=Re{H}. So obviously I can't use that equation. How else can I find N'?

 

[mikelepore]

I memorized those things using B instead of H, but you can convert. Can you write the RMS values of the electric field and magnetic field? You will get the average of the poynting vector S (intensity, or energy per unit time per unit area) if you plug in the RMS values of E and B into any of these:

S = E B / mu0 = E^2 / mu0 c = c B^2 / mu0

 

[watty]

Usually vector E and H are made up and constant (eg E0) multiplied by phase and time dependent parts. You must time average these non-constant parts of the equation. Often this comes down to time-averaging the square of sine/cosine, which gives a multiplicative factor of 0.5.