  When the equatorial spin velocity, $v$, of a charged conducting sphere
approaches $c$, the Lorentz force causes a remarkable rearrangement of the
total charge $q$.
  Charge of that sign is confined to a narrow equatorial belt at latitudes $b
\leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign
occupies most of the sphere's surface. The change in field structure is shown
to be a growing contribution of the `magic' electromagnetic field of the
charged Kerr-Newman black hole with Newton's G set to zero. The total charge
within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to
infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector,
field angular momentum and field energy are calculated for these
configurations.
  Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in
terms of a 19th Century electron model. Classical models with no spin had the
small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton
wavelength, but models with spin take that larger size but are so
relativistically concentrated to the equator that most of their mass is
electromagnetic.
  The method of images at inverse points of the sphere is shown to extend to
charges at points with imaginary co-ordinates.
