Electric field

A charge Q sets up an electric field in the space around it; a charge q placed at a point feels a force because of the field there: F = qE.

The electric field at a point is the force per unit positive test charge, E = lim (q→0) F/q. The test charge is made very small so that it does not disturb the source charges. The SI unit is N C⁻¹ (equivalently V m⁻¹).

The field of a point charge Q is E = kQ/r² along r̂: radially outward for positive Q, inward for negative Q, and the same in magnitude at all points at the same distance (spherical symmetry).

E depends on the source charges and the position, not on the test charge, since F is proportional to q.

For several source charges, add the field each one makes on its own, as vectors: E = E₁ + E₂ + … + Eₙ.

A field is more than a bookkeeping device: when charges accelerate, their influence spreads at the speed of light c, and the field (strictly the electromagnetic field) carries the effect and energy across the delay. The idea of the field was introduced by Faraday.

In a uniform field a charged particle has constant acceleration qE/m. The same field gives an electron an acceleration about 1800 times that of a proton (the ratio of their masses), so unlike free fall under gravity, the time to cover a distance depends on the mass; gravity is negligible beside such forces.