A Magic Electromagnetic Field

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 elec-trodynamic charge distribution surrounding the point electron. The solution obeying this equation everywhere – except the origin – and tending to zero at infinity is Ψ = q/r, but if we move the origin to b this solution becomes Ψ = q (r − b) 2. This solution is harmonic whether q and b are real or complex. To ensure no magnetic monopole, term q must be real, but we now consider the possibility that b = ia where a is real so that b is pure imaginary. Then we shall have both an electric and a magnetic field with F = E + iB = −∇Ψ. Without loss of generality we may orient the z axis along a so that Ψ = q R 2 + (z − ia) 2 1/2 where R 2 = x 2 + y 2 .