Solving Equations in Spherical Coordinates with Elliptic Integrals

[boarie]

Dear gurus

Can anyone kindly enlighten me how to go abt solving the attached equation expressed in spherical coordinates? basically, it describes the magnetic field in the radial direction with r,theta and phi denoting the radius, polar and azimuthal angles.

My problem is that I do not know how to relate this equation to elliptic integral as it is to the power of 3/2. Any help is deeply appreciated.

Thx in advance!

 

[dextercioby]

Here's the trick. U need to use some notations

$$R^{2}+r^{2} =p^{2}$$

$$2rR\sin\vartheta =u$$

One has that $p^2 >0 \ ,\ u>0$.

Then the integral becomes

$$B_{r}(r,\vartheta) =C \int_{0}^{2\pi} \frac{d\phi}{\left(p^{2}-u \sin\phi\right)^{\frac{3}{2}}} = C$$

times the result below. The notation for the complete elliptic integrals is the one Mathematica uses. U can check it out on the Wolfram site and compare it to the standard one (for example the one in Gradshteyn & Rytzik).

Daniel.

 

[dextercioby]

There you go, found it

http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html


Daniel.