How to Prove the Solid Angle Formula for Vector Fields?

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The discussion focuses on proving the solid angle formula for vector fields, specifically the integral equation \int^4 \pi \omega \omega \,d\omega = \frac{4}{3} \pi, where \omega represents a vector. Participants seek hints and clarifications on the physical significance of the formula and its mathematical derivation. The use of LaTeX for formula notation is emphasized, indicating a need for precise mathematical communication.

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Jana
Hello,
I would like to ask you for hints to proof this:

Code:
\int^4 pi \omega \omega \,d\omega =%fraction{4}{3} \pi

where omega is vector.

Do you have any hints for me? (Not seeing for solution, just hints).
 
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Please use our LaTeX code library to note formulas (https://www.physicsforums.com/help/latexhelp/)
This is what I got from your code line, but I'm by no means sure that it is what you meant: ##\int^4_\pi \omega \omega \,d\omega =\frac{4}{3} \pi\,.## Also some explanations would be helpful. You originally posted it in a physics section, so what is physical here?
 

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