In some matter every charge is nailed down where it was born. In other matter the charges are a sea, and a sea will not hold still while a field pushes on it. It moves until the inside is quiet.
⟨ transmission ends ⟩This fragment teaches you to tell a conductor from an insulator, and to say what either one does when a field arrives. By the end you will know why charge on a metal always runs to the outside, and why a metal box keeps its inside perfectly quiet.
Fragment 04 left you on a landscape where nothing moved unless your own hand moved it. Empty space gives charge no road to roll along. Matter sometimes does. Rubbing amber worked in Fragment 00 because the charge stayed where you scraped it. Rub a steel rod held in your bare hand and nothing happens at all.
Below are 2 balls of the same size, one steel and one glass, both standing on glass pedestals so that nothing can leak away underneath. The dropper holds a small spot of charge.
The same spot of charge, dropped on one point of each ball. Where is it a moment later?
Balls 5.2 cm across, one load 4 nC. The grains push each other apart by Coulomb’s law along the surface. On real metal the spreading is over far too fast to watch, faster than anything you could measure with; here it is slowed to about 2 s.
On the glass the spot stayed exactly where you put it. On the steel it left at once, ran to the outside and spread itself evenly the whole way around. Nothing pushed it there except itself.
Here is the reason. The atoms of a metal sit in a fixed lattice, and each one hands its outermost electron to the crowd. Those loose electrons wander the whole solid, roughly one for every atom in it. So charge arriving anywhere on a metal is free to move, and like repels like (Fragment 01), so it pushes apart until it can get no further apart, which is the surface. In glass every electron is held by its own atom. It can lean. It cannot leave.
How far apart are the first 2 families? Below, 2 charged steel balls stand on 2 posts, one copper and one glass, and the dial is the time since they were charged.
Both balls are charged, then left alone on posts whose feet are connected to earth. How long does each one keep its charge?
Each ball drains in the usual way, fast at first and slower as it empties, with 1 µs for the copper post and about 10 years for the glass one. Real glass leaks through the dust and damp on its surface, not through the glass.
A millionth of a second against 10 years, from nothing but the post underneath. Charge crosses a metal more easily than it crosses glass by a factor of about 1020, one of the widest gaps nature offers in anything:
Everything so far started with charge you placed yourself. Now leave the metal alone, with nothing extra on it at all, and bring a charged rod near it.
A charged rod comes near a steel ball that carries no charge at all. What happens to the ball?
Ball 3.8 cm across, held on glass; the rod’s +12 nC is treated as a single point at its tip. The threads and the split charge are the exact answer for a point charge beside a metal sphere.
No charge on the ball, and a pull anyway. Look at what the rod did to the ball’s own charge. Its loose electrons were drawn toward the rod and crowded onto the near face, leaving the far face short of electrons and so positive. Add the 2 faces together and you still get exactly 0. But the negative face is the nearer one, and nearer wins, because halving the distance quadruples the force (Fragment 02). The attraction beats the repulsion and the ball is pulled in.
This rearranging is called induction. It is the honest answer to Fragment 01, where a hanging ball swung toward a charged rod before it touched anything.
Those electrons did not stop where they stopped by accident. Each one keeps moving while any push is left on it, so the crowd settles only when the pushes cancel. Below is a cut through a long steel box with a charged wire beside it, and a probe you can carry anywhere in the picture.
A strong field arrives at the outside of the box. What is the field inside the room?
A slice through a long box and a long wire, both running far out of the page; box 15.5 cm across, wire +8 nC per metre. The skin charge is solved for, not drawn in by hand. Inside the metal and the room the field is exactly 0, so the solver’s leftover arithmetic noise there is shown as 0.
Outside, thousands of newtons for every coulomb. Inside the room, nothing. The wire’s field never got in: the box’s own loose charge slid to its skin, negative onto the near wall and positive onto the far one, and the field of that skin cancels the wire’s field at every single point inside. Not weakened. Cancelled.
A closed conductor used this way is a Faraday cage. It does not have to be solid metal: a mesh does nearly as well, as long as the holes are small compared with whatever you are keeping out.
That is the whole of this fragment in one line. It is not an equation with anything to work out, but a rule about how metal ends up, and it has a name: the field inside a conductor at rest.
Inside means the metal itself, and any empty room the metal closes around. At rest means once the loose charge has stopped moving, which happens almost the instant a field arrives. Those 2 words hold each other up: if any push were left inside, the charges would still be moving, and the metal would not be at rest yet. Here is how the 0 gets built, in numbers kept simple on purpose:
The box you probed did the same with a real bench’s far bigger numbers: about 2,300 N/C arriving at its near wall, and still exactly 0 in the room. Nobody tells the skin how much is coming. A stronger field outside simply moves more charge to the skin, until the cancelling is exact again.
In Fragment 01 a hanging ball with no charge on it swung toward a charged rod before touching it. Why?
Your phone loses its signal inside a steel elevator. Which explanation is the honest one?
You have copper, dry wood, salt water and plastic. Charge each one at a single spot and watch. Which pair spreads the charge out by itself?
You can now sort matter into the 2 families by what a spot of charge does on it, and say what a conductor does when a field arrives: it rearranges its own charge until the inside goes quiet. Fragment 28 builds that quiet into a circuit board, Fragment 37 into a shield.
There is one thing 2 conductors can do that a single one cannot. Bring 2 of them close, keep them apart with an insulator, and charge one of them: each one’s field now reaches the other, and the pair holds far more charge for every volt than either could alone. How much more is Fragment 06.