Speaker
Description
Using MACSYMA—the superb computer calculus program developed at MIT in the 1970s, ‘80s, and ‘90s—I have derived, verified, and meticulously simplified the analytic formulas for all magnetic quantities generated by any system of coaxial, axisymmetric, rectangular-cross-section (RCS), uniform-current-density (UCD) coils. All formulas now have the same constant of integration—zero—verified by differentiating all formulas in every possible permutation. The more complex analytic formulas require the definition of a new function, EI, which is the integral of E, the elliptic integral of the second kind. Note that both E and EI have no singularities—in fact, E varies merely from 1 to π/2! Thus, the accuracy of these formulas is excellent. During these derivations, I derived the analytic formula for the radial component of the magnetic field of a disk, BRDISK. This new formula represents the first advance in analytic formulas of this type since Professor Snow at MIT derived the analytic formulas for any system of coaxial solenoids in1939! I also derived—or perhaps rederived—a simple identity between the elliptic integrals of the third kind of arguments n1 and n2: π (n2, k) = F (k) - π (n1, k). This identity, of course, permits an alternate expression for the formulas for solenoids, disks, and coils.
