Coulomb
In 1785 Charles Coulomb hung a light beam with a ball of elder pith on a silver thread. Next to it he fixed a second such ball and charged both. The balls pushed apart and the thread twisted. Coulomb turned the head of the thread and watched how many degrees it had to be twisted to bring the balls twice as close. It came out four times as many.
This showed that the force between charges falls off as the square of the distance. The unit of charge was named after him in 1881. One coulomb is the charge that a current of one ampere carries in a second, about 6.24·10¹⁸ electrons. A phone battery holds about 14 000 coulombs, and a lightning flash carries about twenty.
| Notation | C |
| Definition | ampere-second · A·s · exactly 1/e elementary charges |
| Reference values | e — 1.602 176 634·10⁻¹⁹ C · 1 A·h — 3600 C · faraday — 96 485 C |
| Introduced | 1881, International Congress of Electricians · in the SI since 1960 |
| Standards | ISO 80000-6 · IEC 80000-6 · SI Brochure 9th ed. |
| Typical values | 1 µC — a spark from a finger · 20 C — lightning · 14 400 C — a phone battery |
01 · Definition
An ampere for a second
Charge Q is the quantity of electricity. If a current of one ampere flows in a wire, one coulomb passes through its cross-section every second. Charge can be positive or negative. Like charges repel, unlike charges attract.
Charge does not appear from nothing and does not vanish. When amber is rubbed with wool, electrons only move from one body to the other. The charge of any body is a multiple of the electron charge e. Since 2019 this number has been exact: 1.602 176 634·10⁻¹⁹ C.
Where are there more coulombs: in lightning or in a phone
On the left are two vessels filled with charge on a logarithmic scale: each division is a thousand times more. The blue dots are electrons. On the right, red bars show the energy of the same charge, also on a logarithmic scale. Energy is charge multiplied by voltage, so the bars and the vessels can disagree. Choose what to compare.
Batteries give their charge in ampere-hours: a current of one ampere carries 3600 C in an hour. A 4000 mAh phone battery holds 14 400 C. Energy is charge multiplied by voltage: 14 400 C at 3.85 V is about 55 kJ, or 15 Wh.
Twice as close — four times as strong
On the left, the balance from the side: a glass cylinder, a beam with a ball hanging on a silver thread, and a second ball fixed next to it. In the middle, the same cylinder from above, with a degree scale on the wall. The red arrow is the force with which the charges push the ball away; the brass one is the force of the thread pulling it back. On the right is the head of the thread: turning it twists the thread harder, and the balls come closer. Measurements are recorded at the bottom right: the angle between the balls and the total twist of the thread. The squares are the numbers from Coulomb's report.
The balls are charged and repel. Turn the head of the thread.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
The faraday is the charge of a mole of electrons, 96 485 C. That is what it takes to deposit 108 g of silver from a solution.
A 4000 mAh battery holds 14 400 C, but at 3.85 V that is only about 15 Wh of energy.
The statcoulomb of the CGS system is about three ten-billionths of a coulomb.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
Since 2019 the SI has fixed the value of the elementary charge: exactly 1.602 176 634·10⁻¹⁹ C. The ampere is now a flow of such charges per second, and one coulomb holds exactly 1/e elementary charges, about 6.24·10¹⁸.
The ampere used to be defined through the force between wires, and earlier still through silver. In 1908 the “international ampere” deposited 1.118 mg of silver per second from a solution, so each coulomb gave 1.118 mg. Today charge can be counted one by one: a single-electron pump moves electrons one at a time at a set frequency.
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