Electric charge

Rub a plastic comb on dry hair and it picks up bits of paper. Rubbing has given it an electric charge. There are two kinds, called positive and negative: like charges repel, unlike charges attract.

Rubbing does not create charge. It moves electrons from one body to the other. The body that gains electrons becomes negative; the body that loses them becomes positive, by the same amount.

Five properties of charge, each worth knowing by name:

• Additivity: charges add like ordinary numbers, with their signs. +3 µC, –5 µC and +1 µC together make –1 µC.
• Conservation: the total charge of an isolated system never changes. Charge only moves around.
• Quantisation: charge comes in whole lumps of e = 1.6 × 10⁻¹⁹ C. Any charge is q = ±ne, where n is a whole number.
• Invariance: charge does not change with speed. Mass grows at speeds near light; charge does not.
• Like repel, unlike attract.

In q = ne, the sign tells you the direction of transfer: a positive body has given away n electrons, a negative body has taken n electrons.

Example: a body carries 5 × 10¹³ extra electrons. q = 5 × 10¹³ × 1.6 × 10⁻¹⁹ = 8 × 10⁻⁶ C, so its charge is –8 µC.

Since e is so tiny, everyday charges contain billions of electrons, and quantisation is not noticed. That is why we can treat large charges as smooth.

Conductors (metals, our body, the earth) let charge move freely. Insulators (glass, plastic, rubber) hold charge where it is put. Connecting a charged conductor to the earth drains its charge away: this is earthing.

Charging by induction: bring a charged rod near a conductor (without touching). The conductor's charges separate. Earth the far side, remove the earth, then remove the rod: the conductor keeps a charge opposite to the rod's.