Friedel Oscillations 2D: Screened Charge-Density Cross-Section

A point charge dropped into a metal is not screened smoothly — the sharp Fermi surface of the conduction electrons forces the induced charge density into a ringing, slowly-decaying oscillation known as a Friedel oscillation. This 2D companion renders the same radially-symmetric density perturbation δn(r) two ways simultaneously: a flat cross-section field colored pixel-by-pixel by r = √(x²+y²), and a signed radial profile curve, both driven by the exact same closed-form Friedel / Thomas–Fermi formulas as the 3D point-cloud version, with a live draggable probe radius and matching readouts.