# Thread: Stokes theorem trouble

1. ## Stokes theorem trouble

Hi all,
I have question that goes as follows:

If $\displaystyle f(\underline{r})$ is a scalar field, use stokes theorem to deduce that

$\displaystyle \int\int_{S} grad f \wedge d\underline{S} = -\oint_{C}fd\underline{r}$

Where C is a space curve bounding a closed space S.
When I look at the equations, I can see that $\displaystyle -\oint_{C}fd\underline{r} = -\int\int_{S} curl \underline{f} * d\underline{S}$, as by Stoke's theorem. However, I don't think that helps just yet. Apart from that, I'm not sure how to approach this question.

Any points in the right direction is greatly appreciated. Thanks in advance!

2. Originally Posted by Silverflow
Hi all,
I have question that goes as follows:

If $\displaystyle f(\underline{r})$ is a scalar field, use stokes theorem to deduce that

$\displaystyle \int\int_{S} grad f \wedge d\underline{S} = -\oint_{C}fd\underline{r}$

Where C is a space curve bounding a closed space S.
When I look at the equations, I can see that $\displaystyle -\oint_{C}fd\underline{r} = -\int\int_{S} curl \underline{f} * d\underline{S}$, as by Stoke's theorem. However, I don't think that helps just yet. Apart from that, I'm not sure how to approach this question.

Any points in the right direction is greatly appreciated. Thanks in advance!
If f is a scalar field, that second equation makes no sense- neither curl f nor f*dS is defined.

However, if you take $\displaystyle \vec{n}$ to be the unit normal at each point on the surface, then $\displaystyle f\vec{n}$ is a vector and $\displaystyle curl f\vec{n}= grad f\times\vec{n}+ f curl \vec{n}$. Try using Stoke's theorem on that.

3. Thanks!