Electric Field & Potential Plotter

Electrostatics sandbox: place point charges and see the electric field and potential they create. Field lines run from + to − charges; the colour map shows the potential as equipotential bands.

How to use (2D)

• Add + / Add − drops a charge; drag any charge to move it; double-click a charge to delete it.
• Charge |q| sets the magnitude of newly added charges.
• Toggle the Potential map, Field lines and Field vectors.
• Drag the white probe to read the local potential V and field |E| (arrow shows direction).
• Release test charge launches a positive test charge from the probe; it accelerates along the field (a = qE), leaving a trail.
• Presets: dipole, two like charges, quadrupole, parallel plates, and a 3D cube octupole.

3D view: tick 3D 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.

Physics (k = 1, arbitrary units): potential V = Σ q_i / r_i, field E = Σ q_i r̂_i / r_i². Field lines never cross, point away from + and into −, and are denser where the field is stronger; equipotential bands are perpendicular to field lines.

Limitations: 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.