Volume in Spherical Coordinates

1. craigory

3
1. The problem statement, all variables and given/known data

express a volume element dV= dx*dy*dz in spherical cooridnates.

2. lanedance

3,307
have a crack mate! any ideas?

3. craigory

3
Is it simply to convert x y and z into corresponding spherical coordinates (ie r cos θ etc)

4. HallsofIvy

40,391
Staff Emeritus
One way to do this is geometric- given specific r, $\theta$, and $\phi$, mark off a small "$\Delta r$", "$\Delta \theta$", "$\Delta \phi$" about the point and caculate its volume.

Another is analytic- determine dx, dy, and dz in terms of r, $\theta$, $\phi$, $dr$, $d\theta$, and $d\phi$, then multiply- but remember that multiplcation of differentials is anti-commutative: $a(r,\theta, \phi)drd\theta= -a(r, \theta, \phi)d\theta dr$.