- #1
yungman
- 5,708
- 240
I want to integrate around a closed circular path on xy plane around the origin. Say the radius is b. So
##\oint d\vec l## where ##d\vec l=\hat{\phi}b d\phi##
1) If I just use polar( or spherical or even cylindrical) coordinates. R=b and
[tex]\oint d\vec l\;=\;\hat{\phi}\int_0^{2\pi} b d\phi\;=\;2\pi b[/tex]
2) Using rectangular co where ##\hat{\phi}=-\hat x \sin \phi +\hat y \cos \phi##
[tex]\oint d\vec l\;=\;b\int_0^{2\pi} (-\hat x \sin\phi+\hat y \cos \phi) d\phi\;=\;0[/tex]
What did I do wrong?
##\oint d\vec l## where ##d\vec l=\hat{\phi}b d\phi##
1) If I just use polar( or spherical or even cylindrical) coordinates. R=b and
[tex]\oint d\vec l\;=\;\hat{\phi}\int_0^{2\pi} b d\phi\;=\;2\pi b[/tex]
2) Using rectangular co where ##\hat{\phi}=-\hat x \sin \phi +\hat y \cos \phi##
[tex]\oint d\vec l\;=\;b\int_0^{2\pi} (-\hat x \sin\phi+\hat y \cos \phi) d\phi\;=\;0[/tex]
What did I do wrong?