Register to reply

Elliptic Integrals

by boarie
Tags: elliptic, integrals
Share this thread:
Sep2-06, 03:12 AM
P: 7
Dear gurus

Can any one 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!
Attached Thumbnails
Phys.Org News Partner Mathematics news on
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Sep6-06, 08:30 AM
Sci Advisor
HW Helper
P: 11,948
Here's the trick. U need to use some notations

[tex] R^{2}+r^{2} =p^{2} [/tex]

[tex] 2rR\sin\vartheta =u [/tex]

One has that [itex] p^2 >0 \ ,\ u>0 [/itex].

Then the integral becomes

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

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).

Sep6-06, 08:56 AM
Sci Advisor
HW Helper
P: 11,948
There you go, found it


Register to reply

Related Discussions
Elliptic integrals Calculus 0
Help needed with an elliptic PDE Differential Equations 6
Approximating Elliptic Integrals on the computer Advanced Physics Homework 0
Elliptic Integral Calculus 3
Elliptic integrals Calculus 4