Assume that I know the value of [tex]\iint_{S} \overrightarrow{F} \cdot \hat{n} dS[/tex] over any surface in [tex]\mathbb{R}^3[/tex], where [tex]\overrightarrow{F}(x,y,z)[/tex] is a vector field in [tex]\mathbb{R}^3[/tex] and [tex]\hat{n}[/tex] is the normal to the surface at any point considered.(adsbygoogle = window.adsbygoogle || []).push({});

Using that I would like to compute [tex]\overrightarrow{F}[/tex]. How can this be done?

P.S. I think I suffices to know [tex]\iint_{S} \overrightarrow{F} \cdot \hat{n} dS[/tex] over the planes perpendicular to the axes.

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# How to inverse surface integral of a vector field

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