Use Stokes' Theorem to find the circulation of F= around the triangle obtained by tracing out the path (6,0,0) to (6,0,6), to (6,4,6) back to (6,0,0).

Question

Use Stokes' Theorem to find the circulation of  F=<7y, 4z, 5x> around the triangle obtained by tracing out the path (6,0,0) to (6,0,6), to (6,4,6)  back to (6,0,0).

anonymous · Answer

$$\int\limits_S (\vec{\nabla} \times \vec{F}) \cdot d \vec{a}=\oint_P \vec{F} \cdot d \vec{l}$$
is stoke's theorem.

anonymous · Answer

You are trying to do $$\int\limits_{}^{}\int\limits_{}^{} curl F dS$$ F = <7y, 4z, 5x> curl F = <-4,-5,-7> dS is a triangle rotating counter-clockwise. (Note X is constant at 6). So if you just look in the YZ plane, it's just a triangle 6 units up. I think you can take a short cut and dS become dA, which is just the area of the triangle. But i'm not 100% certain about that. BTW, to agree with Malevolence, the circulation is $$∮PF⃗ ⋅dl⃗ . $$ which is why we're calculating the other side of the equation.