# Help~ Stoke's Theorem

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!

Last edited:

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

siddharth
Homework Helper
Gold Member
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?