anonymous one year ago ques

1. anonymous

How does Green's Theorem change from the original formula if we consider a clockwise line integral instead of counter-clockwise??

2. anonymous

Original form $\oint_\limits C \phi dx+\psi dy=\iint_\limits R(\frac{\partial \psi}{\partial x}-\frac{\partial \phi}{\partial x})dxdy$

3. anonymous

@IrishBoy123

4. IrishBoy123

you get a minus answer for the integral, ie a minus area!

5. anonymous

$-\iint_\limits R (\frac{\partial \psi}{\partial x}-\frac{\partial \phi}{\partial y})dxdy?$

6. anonymous

so $\iint_\limits R (\frac{\partial \phi}{\partial y}-\frac{\partial \psi}{\partial x})dxdy$ If we go clockwise ?

7. IrishBoy123

yes, its all definitional if you go the other way you get a negative relationship between the area integral and the line integral. so we could all agree from now on that we'll go clockwise, but we could just swicth round Greens Theorem, and life would go on

8. anonymous

Is it like switching the positive and negative charges and things would still work out(it's just a convention)

9. IrishBoy123

indeed