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I have an arbitrary parameterized surface $S(u,v)$ in Cartesian coordinates (with finite area) and the surface passes through origin. There is a very small circular hole of radius $\epsilon$ at the origin.

Is there a way to show that the limit of the following surface integral is finite? $$ \displaystyle \vec{V} = \lim \limits_{\epsilon \to 0} \iint_S \dfrac{dS}{r^2} \hat{r}$$ Here $r$ is the distance between origin and points on our parameterized surface $S(u,v)$. $\hat {r}$ is a unit vector from our surface to origin.

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  • $\begingroup$ What is $\hat{r}$? $\endgroup$ – DrinkingDonuts Nov 15 '18 at 12:07
  • $\begingroup$ $\hat {r}$ is a unit vector from our surface to origin. $\endgroup$ – Joe Nov 15 '18 at 12:16

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