Stoke's Theorem for Cylinder-Plane Intersection and Surface Evaluation

[ngjingtao]

Given the field $$H=\frac{1}{2}cos\frac{\phi}{2}\hat{\rho}-sin\frac{\phi}{2}\hat{\phi}$$,evaluate both sides of Stokes’ theorem for the path formed by the intersection of the cylinder $$\rho = 3$$ and the plane z = 2, and for the surface defined by $$\rho = 3$$, 0<z<2 , and z = 0, 0<$$\rho$$<3.

I have problem at $$\frac{1}{2}cos\frac{\phi}{2}\hat{\rho}$$ part.

when i do line integral , the dot product of rho and phi will gives me zero

but when i do surface integral, after doing the curl, i will get z vector, dot with the surface with z vector also, i will obtain a value but not zero.

i cannot get LHS and RHS equal

Anyone can help me solve this, thanks!

 

[siddharth]

What have you done? The forum rules are that you need to show your work before you get some help.

 

[siddharth]

when i do line integral , the dot product of rho and phi will gives me zero

I don't see how you got that. Can you post the line integral you evaluated?