- #1

- 371

- 28

- TL;DR Summary
- Let ##f(x,y) =\frac{-y}{x^2+y^2} \hat{i} + \frac{x}{x^2+y^2}\hat{j}## for all ## (x,y) \not= (0,0),## and ##C: x= \cos {(t)}, y = \sin{(t)} , 0\leq t \leq 2\pi.##

(a) Show that ##f = \nabla F,## for ##F(x,y)= \tan^{-1}{\bigg(\frac{y}{x}\bigg)}##

(b)Show that ## \displaystyle\oint_C f\cdot dr = 2\pi.## Does this contradict the following corollary 4.6 ? If yes, explain, If no, explain.

I don't have any idea to answer these questions. I am working on it by searching the reference books where similar questions have been solved by authors. Meanwhile, any member of Physics Forums may help me in answering these questions.

Last edited: