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Volume in Spherical Coordinates 
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#1
Feb712, 06:30 PM

P: 3

1. The problem statement, all variables and given/known data
express a volume element dV= dx*dy*dz in spherical cooridnates. 


#2
Feb712, 07:16 PM

HW Helper
P: 3,307

have a crack mate! any ideas?



#3
Feb712, 07:35 PM

P: 3

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



#4
Feb712, 09:20 PM

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Volume in Spherical Coordinates
One way to do this is geometric given specific r, [itex]\theta[/itex], and [itex]\phi[/itex], mark off a small "[itex]\Delta r[/itex]", "[itex]\Delta \theta[/itex]", "[itex]\Delta \phi[/itex]" about the point and caculate its volume.
Another is analytic determine dx, dy, and dz in terms of r, [itex]\theta[/itex], [itex]\phi[/itex], [itex]dr[/itex], [itex]d\theta[/itex], and [itex]d\phi[/itex], then multiply but remember that multiplcation of differentials is anticommutative: [itex]a(r,\theta, \phi)drd\theta= a(r, \theta, \phi)d\theta dr[/itex]. 


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