  An electromagnetic field of simple algebraic structure is simply derived. It
turns out to be the G=0 limit of the charged rotating Kerr-Newman metrics.
These all have gyromagnetic ratio 2, the same as the Dirac electron. The charge
and current distributions giving this high gyromagnetic ratio have charges of
both signs rotating at close to the velocity of light.
  It is conjectured that something similar may occur in the quantum
electrodynamic charge distribution surrounding the point electron.
