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.