Appendix B - A digression on electromagnetic force, divergences of Maxwell equations, and lengths in atomic physics

<!--HTML--><p>In this second appendix we show how the electromagnetic force and the magnetic field can be seen a side effect&nbsp;electrostatics and special relativity, namely the contraction of lengths seen by a particle with a given speed.</p> <p>We then discuss the two divergences in Maxwell equations: firstly, the well known divergence of the energy contained in the electrostatic field of a point charge, leading to the definition of the classical radius of the electron. The second divergence&nbsp;is for a current loop with infinite current density. We show how the inductance of a loop&nbsp;depends on the wire diameter, and diverges for small wire thickness. We show how to treat this&nbsp;divergence for the self-field contribution in codes like ROXIE, when computing the peak field in the coil.</p> <p>The 20th century physics is characterized by two limits: an upper limit to speed given&nbsp; by special relativity and a lower limit to angular momentum given by quantum mechanics.&nbsp; Using these two constants&nbsp; one canbuild a fundamental&nbsp; length (Compton radius) and a adimensionless electromagnetic coupling constant (alpha). The ratio between the classical electron radius and the Compton radius is given by alpha.</p> <p>We then briefly discuss the quantization of the angular momentum to compute the Bohr radius, as an estimate of the atom size. The simple formalism&nbsp;also allows to compute the average speed of electron in the Bohr model, and estimating the associated magnetic field of this&nbsp;current loop. The average speed&nbsp; of the&nbsp; elecron in this semiclassical model is alpha times the speed of light, i.e. the motion is non relativistic.</p> <p>Finally we discuss the enigma of the intrinsic magnetic momentum of the electron, the anomaly in the gyromagnetic ratio.</p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p>