Electric Fields

How the model works

Each point charge q creates a field that points away from positive charges and towards negative ones, with strength falling off as the inverse square of distance (Coulomb's law):

E = k q / r², V = k q / r, k = 8.99×10⁹ N·m²/C²

Fields from several charges add as vectors (superposition), while potentials add as plain numbers. Field lines start on positive charges and end on negative ones. They never cross, and they meet equipotential contours at right angles.

The simulator samples the field on a grid (arrows, with length compressed so that strong and weak regions both stay readable), traces field lines from each positive charge using small RK4 steps, and colours the background by potential. Charges are in nanocoulombs (nC); distances use a 1 m wide view.

Static point charges in a vacuum, drawn in 2-D (a slice through the 3-D field). Very close to a charge the values grow without limit; the probe reports “near charge” there.

Guided experiments

1. Dipole. One +5 nC and one −5 nC charge. Prediction: lines leave the positive charge and curve round into the negative one. Midway between them the field points from + to −, and the potential is zero there. Make a dipole
2. Two like charges. Two +5 nC charges. Prediction: a neutral point exactly halfway where E = 0. Lines bend away from each other, and none join the two charges. Two positives
3. Parallel plates. A row of positive charges facing a row of negative ones. Prediction: between the rows the field is nearly uniform (parallel, evenly spaced arrows), and the equipotentials are nearly straight lines. This is a capacitor. Build plates

Challenge

A +4 nC charge sits at x = 0 and a +1 nC charge at x = 0.6 m. Where between them is the field zero?

References

• OpenStax, University Physics Volume 2, §5.4 “Electric Field” and §7.6 “Equipotential Surfaces”.