Everything you will ever build rests on one fact: there are two kinds, and only two. We searched for a third until our sun grew old. There is no third.
⟨ transmission ends ⟩This fragment teaches you to sort any charged object into one of 2 families, amber-kind or glass-kind, by experiment, and to say the 4 rules that every charge obeys. By the end you will also have seen charge itself, one grain at a time.
Fragment 00 showed you the amber’s pull. The science begins with a push. Rub 2 pieces of amber, hang them side by side, and they lean away from each other. Charge 2 things the same way, and each refuses the other. A plain pull could never do that.
Below, 2 light balls hang on threads. Their coating lets charge move onto them and across them. The amber rod has been rubbed already, and its counter reads what it carries: 40 units of amber-kind charge, written −40. A unit is a small fixed amount, sized further down the page. Each ball has a counter too, and both read 0.
Touch both balls with the same rod. What will they do to each other?
Balls of 30 mg on 15 cm threads, coated to conduct, anchors 4 cm apart. Each touch hands 10 units from the rod to the ball. The rod’s charge sits on its rubbed tip. Runs at quarter speed. A bare ball is drawn to the rod too; the third chamber explains that pull.
Same rod, same kind, and the balls lean apart. Like pushes like. The counters said a second thing. The rod began at −40. Touched once each, the balls hold −10 apiece and the rod is down to −20. Nothing was made and nothing was lost; charge only moved from one thing to another. Keep an eye on the total: in this fragment and every one after it, it never changes.
Now the other rod. Glass rubbed on silk takes on the second kind of charge, the kind the ancestors wrote with a plus sign. Below, ball A still holds its −10. Ball B has been wiped clean, and the glass rod has been rubbed lightly along its whole length, just enough to carry +10.
Ball A carries amber charge. Give ball B glass charge instead. What will the pair do?
Same balls, same threads. Ball A starts at −10, ball B at 0; the glass rod carries +10 spread along its length, so one touch empties it. Two balls that touch share their charge equally. Runs at one fifth speed so the meeting is visible.
Opposite kinds pull. When the balls met, −10 and +10 added to 0, both counters emptied, and with nothing left to push or pull, the pair hung limp. That is why the two kinds carry opposite signs. The signs are bookkeeping: nothing about amber-kind charge is truly negative, and Benjamin Franklin, who chose the names, could have chosen the other way round. What the signs buy you is arithmetic.
Every charged thing ever tested behaves like the amber or like the glass; nothing has ever repelled both rods, so there is no third family. Four rules cover everything you have seen:
One thing may already have caught your eye: a bare ball drawn to the rod before any touch. Below, 1 bare ball, its counter at 0, and the amber rod.
The ball carries no charge. Will anything happen before they touch?
One ball, 30 mg on a 15 cm thread, counter at 0. The rod’s −40 sits on its tip as before. The leap ends in a touch: the ball then takes 10 units and flies off, exactly as in the first chamber. Runs at one eighth speed.
The ball was never empty. Every ordinary thing holds an enormous amount of both kinds of charge, matched so exactly that you feel none of it. Bring a charged rod near and the two kinds shift a little: the side facing the rod turns a little glass-kind, the far side a little amber-kind. The counter still reads 0, because the ball has gained nothing. But the glass-kind side is nearer the rod, and the nearer pull wins. It grows fast as the gap closes, which is why the ball leaps rather than leans. It is the same pull the amber had on the feathers in Fragment 00. Fragment 05 explains which materials let charge shift and which hold it fast.
Rubbing works the same way: it makes no charge, it moves a little from one thing onto the other. The rod reads −40 because the fur it was rubbed on now reads +40.
So what is a unit? Before the number, a fairer question. Is charge a smooth stuff that can be poured in any amount, or does it come in pieces? Below is 1 wire of an ordinary lamp with charge flowing through it steadily, a flow the ancestors called 1 ampere; Fragment 07 owns that word. The slider slows the wire’s clock.
Slow the wire’s clock far enough. Is charge a smooth fluid, or grains?
One wire of an ordinary lamp: 1 A, about 6.24 × 1018 grains passing each second. The slider slows nothing but the clock. Fully slowed, ×1018, about 6 grains cross each second. Dot size and speed are drawn for the eye, not to scale.
Sand, not water. Every grain that crossed carried exactly the same amount of charge, and no one has ever found a smaller piece. The ancestors measured the grain and named it the elementary charge, e. Its size is written in their unit of charge, the coulomb, C:
Read it three ways. First, what it says: e is the smallest step of charge, and every charge ever measured is a whole number of these steps, q = N × e, a rule the ancestors called the quantization of charge. Second, at the bench: the counters’ unit is 0.4 billionths of 1 coulomb, so a ball reading −10 carries about 2.5×10¹⁰ extra electrons. Third, in numbers, kept simple on purpose:
The coulomb is enormous next to anything on this bench: the rod’s −40 units are 16 billionths of 1 C, and still about 10¹¹ grains, which is why charge looked like water until you slowed the clock.
Objects X and Y pull together; Y and Z pull together. What do X and Z do?
You rub 2 neutral things together and one ends up at −3 units. What is the other at?
Could a third kind of charge be hiding somewhere?
Two kinds, in identical grains, moved but never made. What is still missing is the law of the push itself. Bring 2 charges twice as close: how much harder do they push? Coulomb measured it with a balance, and his answer is Fragment 02.