Using Stokes law, calculate the work done along a curve

[skrat]

Wow, it feels so good to understand that! :D

So, the final sign, the result, basically depends on weather the $r_{\phi }\times r_{\theta}$ and normal vector determined by right hand rule match. If they do not, than the result must be multiplied by -1.

Please correct me if I am wrong.

 

[LCKurtz]

Wow, it feels so good to understand that! :D

So, the final sign, the result, basically depends on weather the $r_{\phi }\times r_{\theta}$ and normal vector determined by right hand rule match. If they do not, than the result must be multiplied by -1.

Please correct me if I am wrong.

$$\pm\int_0^{\frac \pi 2} \int_0^{\frac \pi 2}(\nabla \times \vec F) \cdot \vec r_\phi \times \vec r_\theta~
d\phi d\theta$$
We are talking about the choice of the $\pm$ sign in the statement of Stoke's theorem. Whether the final answer of the problem is positive or negative is a different question and it depends on what the integrand is.