- #1

bcjochim07

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## Homework Statement

In spherical polar coordinates, a vector F is given by

**F**=(r*costheta*cosphi)

**rhat**+ (r*costheta*sinphi)

**thetahat**+ (r*sintheta*cosphi)

**phihat**

Check the validity of the divergence theorem for this vector and the volume that is one octant of a sphere radius b.

## Homework Equations

[tex]\oint[/tex]

**F**[tex]\cdot[/tex] d

**A**= [tex]\int[/tex]

_{V}grad[tex]\cdot[/tex]

**F**d

^{3}r

## The Attempt at a Solution

The solution for this problem is in my book, and I am having difficulty following it, I think because it is in polar coordinates, and I am still trying to get used to them.The author proceeds to divide the surface into four area elements:

spherical surface : d

**A**=

**rhat**(b^2)*sintheta*dtheta*dphi

before I go on to any of the other elements, could someone please help me understand how the author derived this expression? Thanks.