The Jar of Leyden

In this fragment you build the first device that stores electricity. By the end you can say how much charge a device holds for every volt pushed across it, grow that number 3 ways, and count the energy it keeps after the power is off.

Every charge on this road so far sat in the open, on a ball or a rod. In the winter of 1745 two experimenters, both after something else, stumbled on a bottle that holds thousands of times more. On the bench: their friction machine, a rubbing globe turned by a crank; a glass jar lined with metal foil inside and out, reached by a hook on top; and a discharge wand, a bent metal bridge on a glass handle, the safe way to draw a spark. Crank, and watch where the charge goes.

The jar kept everything: 0.5 µC a turn, 30 µC after 60 turns, about 1500 rubbed rods' worth, and it gave it all back in one crack. Pieter van Musschenbroek, the professor at Leyden, took that crack through his own body and wrote to Paris that he would not repeat it 'for all the kingdom of France'. Yet almost everyone who rebuilt his jar found it refused to charge at all, and the reason why is the next experiment.

Charge escapes through anything conducting, so the careful thing, everyone agreed, was to stand the jar on wax while charging. The bench has obeyed: same jar, same machine, a wax cake under the jar, and a brass chain hanging from the ground post nearby, in case you disagree.

Insulated, the jar stalled. Chained, it drank, and the 2 readouts moved together: for every + mote forced onto the inner foil, the outer foil pushed one of its own + motes down the chain into the ground, the rearranging from The Conductor and the Insulator. What stays outside is −, exactly as much as the inside holds +. Nothing can enter unless something can leave; Benjamin Franklin proved that pairing on this very jar. And the pairing is the storing: each + mote sits pressed against a − mote through 2 mm of glass, each holding the other down, so the machine can pile in far more than any open ball could hold. That sandwich, 2 conductors kept apart by an insulator, is called a capacitor.

How much does a capacitor hold, exactly? The machine now stays off the bench: only its chain comes in from the edge, carrying a steady trickle of charge. On the bench: the jar you know, a second jar built bigger with wider foil, and a plot of stored charge against voltage that draws itself as a jar fills.

A straight line through 0, mote after mote. A capacitor is not a bucket that fills to a rim: at double the push it holds exactly twice the charge. And the chain moved to the small jar drew a new straight line with a different slope: 2.0 µC per kV for the big jar, 1.2 for the small. That slope is the device's own number, and it has a name.

Read it 3 ways. A definition: stored charge divided by the voltage it stands at. A bench fact: a 2 F capacitor at 3 V holds 6 C. And the slopes you measured, kept round on purpose:

The ladder below shows how enormous: every capacitance from picofarad to farad exists as a real thing you can hold.

Real parts run picofarads to microfarads: capacitance comes hard, and 3 levers grow it. To see the levers, the bench strips the jar to its bones, the way the English did when they pressed lead foil onto both faces of a flat glass pane and called it a Franklin square: 2 bare plates in air, 20 cm square and 2 mm apart, loaded with 40 nC and cut loose, so the charge is trapped. The threads between them show the field, as in The Field. The right plate moves.

The threads knew before the meter. At fixed charge the field does not care about the gap: the threads kept their thickness and only grew longer. Voltage is the climb along a thread, so 4 times the gap is 4 times the volts: same charge, more volts, Q/V fell. Sliding the plate sideways shrank the overlap and did the same. Big and close is the whole secret, and it explains the jar: wide foil, and 2 mm of glass.

The last lever is the insulator itself. Franklin went looking for where the jar's charge sits: he poured a charged jar's water into a second jar, and the second gave no shock, while the first, refilled, struck as hard as ever. The force of the bottle stays with the glass, he concluded. So ask the plates: the same trapped 40 nC, and a slab of glass beside the gap.

Glass cannot conduct, but its atoms can stretch. In the gap's field each atom leans, so the slab's faces grow a thin skin of bound charge, − facing the + plate, + facing the −. That skin cancels most of the field inside the glass: the threads thinned, and the trapped 40 nC ended at a seventh of the volts, so Q/V grew 7 times. The multiplier, written ε_r, is the material's own: about 7 for this glass, 80 for water, thousands for the ceramics inside modern parts. All 3 levers fit in 1 line:

One question is left: 60 turns of crank were real work. Where did the work go? The energy map of The Potential answers once you pay the bill by hand: a small 0.1 nF capacitor, a tong carrying charge in 2 nC pinches, and a plot of voltage against charge that shades what you have paid.

The first pinch crossed a dead capacitor, almost free. The last fought the full push. The price climbed along the straight line, so the average pinch paid half the final voltage, and the whole bill is the triangle under the line: half of the rectangle Q × V.

0.38 J sounds small for the most feared instrument in Europe, and it is: the terror was speed, the whole store spent in about 1 µs, hundreds of kilowatts for an instant. And the store waits: a capacitor keeps its charge until a path lets it go, sometimes weeks after the power is off, and a supply's storage capacitors hold 100 jars' worth. So a bench discharges big capacitors before fingers go near, and ½CV² is the number that says why.

When you are ready, test yourself:

The jar spends everything in one crack, and then it is done. To light a lamp you need a push that does not die: a pump for charge that works on, hour after hour. It was found, of all places, in a twitching frog's leg. Next, The Frog and the Pile.