# The Magnitude of the Poynting Vector

General question: Is the magnitude of the poynting vector equal to the intensity of an electromagnetic wave? I know that I= average S which makes me think that I cannot simply assume that that their magnitudes are equal!?

The Poynting vector gives the instantaneous quantity representing power/area (which does have the same units as intensity) whereas, indeed, intensity (as it is typically defined) is the time averaged value of the magnitude of the Poynting vector.

That makes sense, I guess the thing that is throwing me off is the "time-average".

Intensity = time average of S
I = <S>
I= (1/2)*c*epsilon not*Emax^2

Can I say then that
magnitude of I = magnitude of S

or would I have to say

magnitude of I = (1/2)*c*epsilon not*Emax^2 = (1/2) * S

Can I say then that
magnitude of I = magnitude of S

or would I have to say

magnitude of I = (1/2)*c*epsilon not*Emax^2 = (1/2) * S

You could say that the magnitude of I is equal to 1/2 of the amplitude of the Poynting vector, but that's it. One is a time-dependent quantity and one is not.

thank you!!