Doubts on Exercise Wording: Energy Density & Poynting Vector

[lorenz0]

Homework Statement

In a certain place on Earth, the magnitude of the magnetic field of solar radiation is equal to $B$.
Calculate the average energy density of solar radiation in that area and the amplitude of the Poynting vector.

Relevant Equations

$u=\varepsilon_0 (cB)^2$, $S=\frac{B^2 c}{\mu_0}$

I have doubts about the wording of the exercise:

(1) energy density is $u=\varepsilon_0 (cB)^2$ but since the question asks for mean energy density should I perhaps average over $cos^2 (\omega t)$ (there due to the $B^2$) and thus use $<u>=\frac{1}{2}\varepsilon_0 (cB)^2$?

(2) it seems to me that usually, due to the rapid changing of the electric and magnetic fields, one is interested in the mean of the amplitude of the Poynting vector $<S>=\frac{B^2 c}{\mu_0}$, so perhaps that is the one I should compute (even if the text doesn't say so)?

I would be grateful for your feedback.

 

[tech99]

I presume the magnetic field quoted is the RMS field. This is the only meaningful term to use because the wave shape of the radiation is not known, being noise-like.
Therefore I think the average energy density may be calculated direct from that value without further averaging.