I am asked to calculate the pointing vector for the following fields:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec{B}=k^2 \frac{e^{ikr}}{r} \left( 1+\frac{i}{kr} \right) \hat{r} \times \vec{p_{\omega}}[/tex]

[tex]\vec{E}=\frac{i}{k} (\vec{\nabla} e^{ikr}) \times \left( \frac{k^2}{r} \left(1+\frac{i}{kr} \left) \hat{r} \times \vec{p_{\omega}} \left) + \frac{i}{k} e^{ikr} \vec{\nabla} \times \left( \frac{k^2}{r} \left( i +\frac{i}{kr} \right) \hat{r} \times \vec{p_{\omega}} \right) [/tex]

We know that:

[tex]\vec{S} = \frac{c}{4 \pi} Re(\vec{E}) \times Re(\vec{B}) [/tex]

We know that:

I can figure out [tex]Re(\vec{B})[/tex] assuming that P_omega points in the z direction:

[tex]Re(\vec{B})=k^2 p_{\omega} \frac{e^{ikr}}{r} sin \theta \hat{\phi} [/tex]

since the imaginary term in B vanishes when taking the real part.

I am not sure how to calculate the real part of E, any thoughts would be appreciated.

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# Poynting vector

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