Electromagnetic magic: The relativistically rotating disk

A closed form analytic solution is found for the electromagnetic field of the charged uniformly rotating conducting disk for all values of the tip speed $v$ up to $c$. For $v=c$ it becomes the magic field of the Kerr-Newman black hole with $G$ set to zero. The field energy, field angular momentum, and gyromagnetic ratio are calculated and compared with those of the electron. A new mathematical expression that sums products of three Legendre functions, each of a different argument, is demonstrated.

Figure 1

(a) Electric lines of force for the Kerr-Newman potential. The density of lines reflects the strength of the field. (b) Magnetic lines of force for the Kerr-Newman potential. The density of lines reflects the strength of the field.