The Effect of Charge Discretization on the Electrical Field Inside a Conductor.

The article investigates how the electric field inside a conductor varies with the number of discrete charged particles, challenging the common textbook assertion that this field is zero. It demonstrates that a nonzero electric field persists near the conductor’s surface within a shallow depth λ, which decreases inversely with the number of charges and is on the order of the spacing between these charges. The study analyzes this effect in both two-dimensional and three-dimensional models, estimating λ based on charge distributions and lattice spacing, and concludes that the classical continuum approximation breaks down near the surface due to charge discretization. This work provides a refined understanding of electrostatics by highlighting the impact of charge quantization on the internal electric field of conductors.