16.13: Coordinate Systems
- Page ID
- 107072
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Cartesian coordinates
2 dimensions: area element: \(dA=dx.dy\).
3 dimensions: volume element: \(dV=dx.dy.dz\).
Polar coordinates
- \(x=r\cos\theta\)
- \(y=r\sin\theta\)
- \(r^2=x^2+y^2\)
- \(tan \theta=y/x\)
- \(dA=r.dr.d\theta\)
Spherical coordinates
- \(x=r\sin\theta\cos\phi\)
- \(y=r\sin\theta\sin\phi\)
- \(z=r\cos\theta\)
- \(r^2=x^2+y^2+z^2\)
- \(\theta=\cos^{-1}\left[\frac{z}{\sqrt{x^2+y^2+z^2}} \right]\)
- \(\phi=\tan^{-1}\left(\frac{y}{x}\right)\)
- \(dV=r^2\sin{\theta}dr.d\phi.d\theta\)