Assume that I know the value of \iint_{S} \overrightarrow{F} \cdot \hat{n} dS over any surface in \mathbb{R}^3, where \overrightarrow{F}(x,y,z) is a vector field in \mathbb{R}^3 and \hat{n} is the normal to the surface at any point considered.
Using that I would like to compute...
Sorry for making this so weird and thank you for all the effort so far. You answered my original question so don't feel to obligated to answer this one if you think I'm making this too complicated.
As for the light source I described - I had pulled it out of my head. The idea was to get a...
Thanks. Again cleared a bit on what's going on. However I meant something a bit different - the hemisphere I though of was suppose to be the one described by \{ (x,y,z) : x^2 + y^2 + z^2 = r^2 \textrm{ and } y \geq 0\}. The whole idea was to get a situation where the flux will be non-uniform...
Great! Now I'm starting to get it!
So in principal to compute \frac{dQ}{dV} I need to express energy as a function of volume and use the definition above.
I'll ask one last thing though. The main reason why I'm trying to understand this is because a lot of quantities in radiometry are defined...
Thanks for the answer.
You are right - I meant derivative. This issue aside, I was hoping for a more "mathematical" answer - what do you mean by taking derivative with respect to area/volume? What is the definition here?
This is annoying me beyond comprehension.
What precisely does one mean by writing:
- \frac{dP}{dA} for a power transferred via unit area of the surface (P is power here)
- \frac{dQ}{dV} for a energy density (Q is energy here)
and how using those formulas can one calculate the defined quantities?