We present an approach to analyze the electrodynamics of nuclear matter in bulk using the relativistic Thomas–Fermi equation. We generalize to the case of N ≃ (m Planck /m n )3 nucleons of mass m n an approach well tested in very heavy nuclei (Z ≃ 106). Particular attention is given to implement the condition of charge neutrality globally on the entire configuration, versus the one usually adopted on a microscopic scale. As the limit N ≃ (m Planck /m n )3 is approached the penetration of electrons inside the core increases and a relatively small tail of electrons persists leading to a significant electron density outside the core. Within a region of 102 electron Compton wavelength near the core, surface electric fields close to the critical value for pair creation by vacuum polarization effect develop. These results can have important consequences on the understanding of physical process in neutron star structures as well as on the initial conditions leading to the process of gravitational collapse to a black hole.