My question about the sum of the electrons' magnetic moments in a wire(What is the sum of the electrons' magnetic moments in a wire?) had an answer which disappeared later. The answer was - if I understood right - that were is a moment in sum.
If there is a moment, could this explain the Lorentz force?
No. The Lorentz force $$ \vec F = q\left( \vec E + \vec v \times \vec B \right) $$ describes the interaction of a charge with electric and magnetic fields. A magnetic dipole moment is a convenient way to describe the source term for a very common field distribution — there are tons of problems where you compute the magnetic field for a rotating charged sphere and discover it's a dipole. However there's no way that you can start from an arrangement of dipole fields and produce a monopole field. The charge is in some way "more fundamental" than the magnetic moment.
The electromagnetic induction of a moving charge in a magnetic field is based on the electron’s magnetic moment. The magnetic field turns the magnetic moment of the electron in the direction of the magnetic field. The motion of the electron undergoes a - predictable and perpendicular on the two vectors of the velocity and the magnetic field - acceleration according to the cross product of this two vectors. This acceleration leads out to the emission of a photon from the electron (Bremsstrahlung). As the photon has a pulse, this pulse reduces the velocity of the electron, and also acts against the momentum change of the electron’s magnetic moment by the external magnetic field gyroscope effect. This process is repeated periodically until the kinetic energy of the electron is consumed.
