Electric Field & Potential Plotter

Place up to 12 signed charges and explore the regularized 3D Coulomb potential. The 2D view is the z=0 plane; positive y points upwards. Draw field computes the selected potential bands and plane streamlines. Drag charges or the white probe; double-click a charge to delete it. The charge magnitude (0.000001–100) applies to additions and presets. Layers and deletion controls are in the menu; charge values are available in that menu.

The model uses k=1 and ε=0.01: V=Σq/√(r²+ε²), E=ΣqΔr/(r²+ε²)^(3/2), so E=−∇V also inside the regularized core. Units are normalized, not calibrated SI. Colors show signed potential bands; streamlines, arrow lengths and seed counts are visual choices, not exact flux density or field-strength scales. Coordinates and potential are sampled in a 3D point-charge model, not a logarithmic 2D line-charge model.

Presets include dipole, like charges, quadrupole, two rows of charges (not continuous conducting plates), and a checkerboard cube octupole. In 3D, spheres are schematic; arrows show the field direction. Ctrl/Meta plus wheel zooms, ordinary wheel scrolls. In 2D with off-plane sources, only the in-plane components and constrained plane streamlines are drawn; |Exy| is the in-plane magnitude.

The optional test particle has positive q/m=1, starts at rest at the probe, and is constrained to z=0. Fixed-step velocity Verlet (Δt=0.0005/√max(1,Σ|q|)) advances according to elapsed model time, without an artificial speed cap. H is kinetic plus potential energy in the prescribed static field. Pause stops motion; Release starts again at the probe. Motion stops near a source (distance 0.14) or at the plotting boundary. Sources do not move and collisions/backreaction are not modeled. Edits stop and clear the old trajectory; hidden tools stop motion. Numerical steps retain pending time, with at most 2048 steps per frame and at most 1500 displayed trail points.

Input drafts, charges, probe, layers and view mode survive navigation/reload within the platform state limits. The trajectory and camera do not. A finite numerical trace and pixel map are approximations; especially close to sources, examine resolution and core assumptions.

A coarse potential preview appears immediately, including after source edits and reload. It samples at most 110×75 points; Draw field computes the finer map and selected field lines. Coordinates stay equally scaled. Charge values and deletion controls are in Layers and charges. Only source/probe inputs, layer choices and mode are stored; the calculated map, test-particle trajectory and camera are not.