- #1

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What justification is there for taking the time average of the wave?

I know we do this to find the energy of an EM wave, but I haven't seen this before in any of my courses.

Isn't this a violation of conservation of energy?

If I remember correctly, If

**E**=Acos(w(

**r**,t)) and the energy density is 1/2ε|

**E**|^2 , then the energy density = 1/2ε|Acos(w(

**r**,t))|^2. We can do the same for

**B**- they are in phase and so then the net energy density must vary as cosine^2. Which can't make sense if it is to agree with cons. of energy. As far as I know from mechanics, the total energy of a closed system is always constant and independent of time.

Yet for these waves we take the time average. Why?

I'm assuming I'm wrong here - I just want to know where the time averaging idea came from, so i can learn how it is derived/proven.