In classical electrodynamics, extended with gradients of the electric and magnetic fields, a linear soliton is presented which bears features of the Kerr-Newman electron of electro-gravity. This is considered as a model for the electron, having a ring shape, with diameter equal to the Compton length ħ/mc and thickness smaller by the fine structure constant. The soliton has a finite mass, a spin-½, a g = 2 factor, and an electric quadrupole moment that is also “twice too large”. From this setup, all relativistic corrections to the classical version of the Pauli Hamiltonian are derived. There appears an additional, spin-dependent quadrupolar force that may vanish on the average. Particle-antiparticle annihilation may become explained on the basis of electromagnetic attraction.