Electric Charge

Two protons a centimetre apart push each other apart with a force about 10³⁶ times their gravitational pull. Mass can’t explain that. Particles carry a second property: electric charge.

A force much stronger than gravity#

Electrons (9.11 × 10⁻³¹ kg), protons (1.673 × 10⁻²⁷ kg) and neutrons (1.675 × 10⁻²⁷ kg) all attract gravitationally. But two protons 1 cm apart repel with about 2.3 × 10⁻²⁴ N, whereas gravity between them is only about 1.9 × 10⁻⁶⁰ N. Two electrons repel equally strongly. Two neutrons only attract, with exactly the tiny gravitational force. The extra force is the electric force, and the property responsible is charge; neutrons have none.

Two kinds of charge#

A proton and an electron 1 cm apart attract with the same 2.3 × 10⁻²⁴ N. Their charges are equally strong but of opposite kinds, and packed together they cancel. By convention the proton’s charge is called positive and the electron’s negative: the labels mean “opposite”, not “more” and “less”.

Unit, quantization and conservation#

Charge is quantized

A body with n₁ protons and n₂ electrons has charge (n₁ − n₂)e. Every known charged particle carries a whole multiple of e, so charge changes only in steps of e. These steps are tiny: rubbing a glass rod gives charges of about a microcoulomb, roughly 6 × 10¹² electrons, so we usually treat charge as continuous.

Charge is conserved

The total charge of an isolated system never changes. Charged particles can be created or destroyed, but only in ways that keep the net charge the same: in beta decay a neutron becomes a proton and a new electron, zero before and after.

Charging by friction#

The Greeks knew around 600 BC that amber rubbed with wool attracts bits of straw. Combs through dry hair, cars driving through air, paper running through a press all get charged the same way: rubbing transfers some electrons from one body to the other. Rub glass with silk and electrons move from the glass to the silk; the glass is left positive, the silk negative.

Induction

Why does a charged rod pick up uncharged paper? A positive rod pulls the paper’s electrons toward its near edge, leaving the far edge positive. This redistribution is induction. The attracted negative charge is closer than the repelled positive charge, so the attraction wins.