Place point charges in 3D space and watch Coulomb field lines trace themselves from + to −. Includes a potential heat-map plane, a movable probe that gives the exact field E, potential V and force at any point, and animated field flow.
Each charge qᵢ makes a field E = k qᵢ r̂ / r² with k = 8.9875517923×10⁹ N·m²/C²; fields from several charges simply add (superposition). The potential is the scalar sum V = Σ k qᵢ / rᵢ, and E = −∇V.
Field lines are traced with 4th-order Runge–Kutta, always stepping along the local field direction. They start on a Fibonacci sphere around each positive charge, with the number of lines proportional to |q| — so line density honestly represents field strength (Gauss's law). They end on negative charges or leave the box. When every charge is negative, lines are traced backwards from the negative charges instead.
The coloured plane shows V on z = 0: red for positive potential, blue for negative, with contour bands as equipotentials (lines always cross them at right angles). Units: positions in centimetres, charges in nanocoulombs.
Worked example: a single +1 nC charge at the origin, probe at 1 cm: E = 8.988×10⁹ × 10⁻⁹ / 0.01² = 89,875 N/C, V = 898.8 V.