Charge distributions create invisible electric fields that exert forces on other charges. Field lines reveal the field's direction and strength at a glance — they point away from positive charges, toward negative ones, and never cross each other.
The field at any point is the vector sum of each charge's contribution: E = k·q·r̂/r² (Coulomb's law). Field lines are integrated numerically using Euler steps. Equipotential surfaces — perpendicular to field lines — are superimposed as contour curves.
Left-click to place a positive charge (+), right-click for a negative charge (−). Drag charges to reposition them. Use the charge slider to vary magnitude. Toggle Equipotentials to see the voltage landscape.
Michael Faraday introduced field lines in 1831 to visualise electromagnetic forces he could not mathematically describe. When Maxwell later provided the mathematics — Maxwell's equations — field lines became one of physics' most powerful tools. They directly predict how antennas, capacitors and particle accelerators work.