Electric Field & Potential Plotter

<p>Electrostatics sandbox: place point charges and see the <b>electric field</b> and <b>potential</b> they create. Field lines run from + to − charges; the colour map shows the potential as <b>equipotential bands</b>.</p><p><b>How to use (2D)</b></p><ul><li><b>Add + / Add −</b> drops a charge; <b>drag</b> any charge to move it; <b>double-click</b> a charge to delete it.</li><li><b>Charge |q|</b> sets the magnitude of newly added charges.</li><li>Toggle the <b>Potential map</b>, <b>Field lines</b> and <b>Field vectors</b>.</li><li>Drag the white <b>probe</b> to read the local potential V and field |E| (arrow shows direction).</li><li><b>Release test charge</b> launches a positive test charge from the probe; it accelerates along the field (a = qE), leaving a trail.</li><li><b>Presets</b>: dipole, two like charges, quadrupole, parallel plates, and a 3D cube octupole.</li></ul><p><b>3D view</b>: tick <b>3D</b> to see the charges as spheres with field-line streamlines traced through space. Drag to rotate, Ctrl+wheel to zoom, right-drag to pan. Add charges and presets work in 3D too.</p><p><b>Physics</b> (k = 1, arbitrary units): potential <code>V = Σ q_i / r_i</code>, field <code>E = Σ q_i r̂_i / r_i²</code>. Field lines never cross, point away from + and into −, and are denser where the field is stronger; equipotential bands are perpendicular to field lines.</p><p><b>Limitations</b>: it uses the 3D 1/r potential evaluated in a 2D plane for the 2D view (true 2D line charges would give a ln r potential); a soft core near each charge avoids the singularity; and the released-charge motion is a qualitative integrator.</p>