Static electricity arises from the imbalance of electric charges at rest on the surface of materials. The fundamental interaction is the Coulomb force F = kq1q2/r², where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant. Charge accumulation via the triboelectric effect (contact and separation of dissimilar materials) underlies everyday phenomena from balloon-on-hair attraction to lightning, which discharges hundreds of coulombs in milliseconds.
This simulation visualises charge distributions on conductors and dielectrics, draws electric field lines, and renders equipotential surfaces. You can place positive and negative charges, observe induced polarisation in dielectrics, and see how conductors redistribute surface charge to make their interior field-free.
What is Coulomb's law?
Coulomb's law gives the electrostatic force between two point charges: F = kq1q2/r², where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C². The force is attractive for opposite charges and repulsive for like charges, and falls off with the square of distance. Two 1-coulomb charges 1 metre apart exert a force of nearly 10 GN—about the weight of a million tonnes.
What is the triboelectric effect?
The triboelectric effect is the transfer of electrons between materials upon contact and separation. Different materials have different affinities for electrons (described by the triboelectric series): rubbing a glass rod with silk leaves the glass positively charged and the silk negatively. The effect scales with contact area and can generate voltages of thousands of volts, though the total charge (and energy) is small.
Why does charge reside only on the surface of a conductor?
Inside a conductor in electrostatic equilibrium, free electrons redistribute until the net electric field is zero (otherwise they would continue moving). By Gauss's law, if E = 0 inside then the enclosed charge density is also zero. All excess charge therefore resides on the outer surface, distributed so that the surface is an equipotential. This redistribution happens within nanoseconds for good conductors.
Electric field lines are a visualisation tool introduced by Faraday. They originate on positive charges and terminate on negative charges; their direction at any point shows the direction of E, and their spacing indicates field strength (closer lines = stronger field). They never cross (the field has a unique direction at each point), and they are always perpendicular to conductor surfaces in electrostatics.
An equipotential surface is a surface on which the electric potential V is constant. No work is done moving a charge along an equipotential. Electric field lines are always perpendicular to equipotentials. Around a point charge, equipotentials are concentric spheres. Conductor surfaces are always equipotentials in static conditions. Understanding equipotentials is essential for designing capacitors and electrostatic lenses in electron microscopes.
In a thundercloud, collision and separation of ice crystals and graupel particles (via the triboelectric effect) separates charge: positive near the top and negative near the base. When the electric field reaches about 3 MV/m (the breakdown strength of air), a stepped leader propagates downwards. When it connects to an upward streamer from the ground, a return stroke carrying 20,000–300,000 A surges upward, releasing up to 10 GJ of energy.
Electrostatic induction is the redistribution of charges in a conductor caused by a nearby charged object, without direct contact. A positively charged rod held near a neutral metal sphere attracts electrons to the near side and repels positive charge to the far side. If the sphere is then grounded (allowing the excess positive charge to flow away) and the ground removed before the rod, the sphere retains a net negative charge.
Industrial electrostatic precipitators remove particulates from exhaust gases by applying a strong electric field (50–100 kV) between a discharge electrode (corona) and a collection plate. The corona ionises air, and ions attach to dust particles, giving them charge. The Coulomb force then drives charged particles to the collection plates, where they are periodically dislodged. Modern units achieve removal efficiencies above 99.5% for particles down to 0.1 μm.
A Van de Graaff generator uses a moving belt to continuously transport charge onto a large metal sphere, accumulating static charge until the electric potential reaches hundreds of thousands or millions of volts. The first large Van de Graaff accelerator (built 1931) reached 1.5 MV. Modern electrostatic accelerators use Pelletron chains instead of belts and can reach 25 MV, used in nuclear physics and ion implantation for semiconductor manufacturing.
In a dielectric (insulating) material, no free electrons exist, but the bound positive and negative charges within each molecule can shift slightly under an applied electric field, creating electric dipoles. This polarisation produces an internal field opposing the applied field, reducing the net field inside the dielectric. The ratio of capacitance with and without the dielectric is the relative permittivity (dielectric constant) εr, which is 80 for water and 4–8 for most plastics.