Electrostatics

Electrostatics is a branch of physics that studies electric charges at rest or moving slowly, the forces between them, and the electric fields and potentials they produce. It covers charge distribution, the interaction of charges with materials, and how fields propagate in vacuum and in matter. The subject is largely governed by classical electromagnetism and underpins many practical devices and processes.

One central relation is Coulomb's law: F = k q1 q2 / r^2, where k is 1/(4πε0). For a test charge q in an electric field E, the force is F = qE, and the field of a point charge q is E = k q / r^2 r_hat. Electric potential V is defined so that E = -∇V; the potential difference V(b) − V(a) equals the negative line integral of E along a path between a and b.

Gauss's law provides a global statement about the field: ∮ E · dA = Q_enclosed / ε0. In materials, the displacement field D and the relation D = ε E apply, with ε = ε0 ε_r. Dielectrics reduce the effective field inside them, and conductors in electrostatic equilibrium carry excess charge on their surfaces, with the interior field vanishing. Charge can be transferred by conduction, friction, or induction.

Applications of electrostatics include electric shielding via Faraday cages, electrostatic painting and coating, and electrostatic precipitation to remove particulates. The technology also underpins xerography and various sensors and detectors. The principle of superposition allows complex charge configurations to be analyzed by summing contributions from individual charges.