The mechanism accelerating cosmic rays in the Milky Way Galaxy and galaxy clusters is identified and described. The acceleration of cosmic rays is a purely electrostatic process which operates up to the maximum energies of $10^{23}$ $eV$ in galaxy clusters. Galactic cosmic rays are accelerated in a pervasive electrostatic field active in the whole Galaxy except in restricted regions shielded by interstellar and stellar plasmas as, for instance, the region occupied by the solar system.
It is proved that the energy spectrum of the cosmic radiation in the $Milky$ $Way$ $Galaxy$, in the region where the solar system resides, has a constant spectral index comprised between 2.64-2.68 and the maximum energies of Galactic protons are $3.0 \times 10^{19}$ $eV$. The agreement of these results with the experimental data is discussed in detail and underlined.
The various physical processes that maintain the stability of the electrostatic structure in the $Milky$ $Way$ $Galaxy$ are the same that generate the Galactic magnetic field.
Accordingly, the intensity, orientation and direction of the Galactic magnetic field are evaluated. The results of the calculation are compared with the observational data, optical and mostly radio astronomy data. The accord of the intensity, orientation and direction of the observed magnetic field with calculation is excellent.