- #1
Karl Karlsson
- 104
- 12
- Homework Statement
- Consider the vector field
##\vec v = exp(\frac {xy} {r_0^2}) [\frac {z} {r_0^2} (x\vec e_1 + y\vec e_2) + \vec e_3] + \frac {1} {r_0} (x\vec e_2 - y\vec e_1) + cos(\frac {z} {r_0})\vec e_3##
where ##r_0## is a constant with dimension length.
a) Calculate ##\nabla\cdot\vec v## and ##\nabla\times\vec v##.
b)Calculate the circulation integral $$\oint_Γ \vec v \,d\vec S$$ where Γ is the curve that is parameterized by ## x = r_0cos(t), y = r_0sin(t), z = r_0cos^2(2t), (1 < t < 2\pi)##
- Relevant Equations
- ##\vec v = exp(\frac {xy} {r_0^2}) [\frac {z} {r_0^2} (x\vec e_1 + y\vec e_2) + \vec e_3] + \frac {1} {r_0} (x\vec e_2 - y\vec e_1) + cos(\frac {z} {r_0})\vec e_3##
My attempt is below. Could somebody please check if everything is correct?
Thanks in advance!
Thanks in advance!