An apparent connection is reported between the magnetic field strengths inside an electron, in newly born pulsars, and the sun. It is argued that the upper limit to the strength of magnetic field which seems to exist is that which would permit emission of a photon at the non-relativistic electron gyrofrequency, with energy of the order of the electron rest mass. The strongest magnetic fields at the surface of polar regions of pulsars conform to this. By equating approximately the rest mass of an electron to its magnetic energy, the same magnetic field is found inside the electron. It is proposed that magnetic field building ‘blocks’ called M-particles are formed by a variant of the electron-positron spin-zero annihilation. The particles become as tightly stacked as possible to form the macroscopic magnetic field of the newly born pulsar. The sun’s present magnetic moment is described by a pulsar-sized object at its centre, with the maximum packing of M-particles. The hypothesis may have a bearing on the formation of magnetic fields in celestial bodies, and on the secular variation of the magnetic fields of the sun and the Earth.