(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In spherical polar coordinates, a vector F is given byF=(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.

2. Relevant equations

[tex]\oint[/tex]F[tex]\cdot[/tex] dA= [tex]\int[/tex]_{V}grad[tex]\cdot[/tex]Fd^{3}r

3. The attempt at a solutionThe 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 : dA=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.

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# Help w/ Seaborn's Mathematics for the Physical Sciences

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