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Say I have a source of radiation placed at my origin and I know its power is spread uniformly about 2*pi at a certain frequency, I believe this is also called luminosity. (or a 2D equivalent)

This means if I put a shell around the source and collect this power, then as long as the shell is closed and contains the origin, I collect all my power back - implying there is some vector field which is subject to the divergence theorem - is this the Poynting vector?

I want to know what this field is for a point source, and get to grips with the working of the vector field, because ultimately I am planning to find the incident intensity over a complicated curved surface (I am hoping to integrate the dot product of this field with my normal to the surface).

I hope this make sense and I haven't asked a question without giving enough information because I am a little hazy on Poynting vectors.

Thanks