Volume in Spherical Coordinates

[craigory]

Homework Statement

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

 

[lanedance]

have a crack mate! any ideas?

 

[craigory]

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

 

[HallsofIvy]

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: $a(r,\theta, \phi)drd\theta= -a(r, \theta, \phi)d\theta dr$.