A PEP model of the electron
  One of the more profound mysteries of physics is how nature ties together EM fields to form an electron. A way to do this is examined in this study. A bare magnetic dipole containing a flux quantum spins stably, and produces an inverse square E= -vxB electric field similar to what one finds from charge. Gauss' law finds charge in this model, though there be none. For stability, a current loop about the waist of the magnetic dipole is needed and we must go beyond the classical Maxwell's equations to find it. A spinning E field is equivalent to an electric displacement current. The sideways motion of the spinning E (of constant magnitude) creates a little-recognized transverse electric displacement current about the waist. This differs from Maxwell's electric displacement current, in which E increases in magnitude. The sideways motion of E supports the dipolar B field, B=vxE/c^2. Beyond the very core of the magnetic dipole, each of these two velocities is essentially c and vxE/c^2 = vx(-vxB)/c^2 = B, the spinning E field wholly sourcing the dipolar B field. The anisotropy of the vxB field is cured by precession about an inclined axis. Choosing a Bohr magneton for the magnetic dipole and assuming it spins at the Compton frequency, Gauss' law finds Q = e. The vxB field, normally thought to be solenoidal, becomes instead a conservative field in this model. Charge is recognized as merely a mathematical construct, not fundamental but nevertheless useful. With charge deleted, and with addition of the transverse electric displacement current, Maxwell's equations can be written in terms of the E and B fields alone. 
R. L. Collins