Charging by Friction, Contact & Induction

Press two dissimilar materials together and their outermost electrons feel two different pulls; at every point of genuine contact a few electrons cross to the material that grips them harder and stay there. Rubbing does not create that transfer, it multiplies it, because two rough surfaces sliding over one another meet at far more points than two surfaces merely laid together. The triboelectric series lists materials in the order they surrender electrons — hair and wool near the giving end, polythene and PTFE near the taking end — so wool rubbed on polythene leaves the polythene negative and the wool equally positive. The amounts are tiny in electron terms and large in electrostatic ones. Take the rod above at −2.0 × 10⁻⁸ C: a 25 g polythene rod contains about 8.6 × 10²⁴ electrons, so the 1.2 × 10¹¹ that crossed are about 1.5 parts in 10¹⁴ of them. Because polythene is an insulator, those electrons stay in the patch where they landed instead of spreading over the rod.

A metal behaves differently, because its conduction electrons roam the whole body. Touch a charged conductor to a neutral one and the pair becomes a single conductor; electrons flow until it reaches one common potential, and both objects come away carrying the same sign as the charged one. For two identical spheres symmetry does the work — whatever one has the other must have — so the total divides in half, and every further touch halves again. For unequal spheres size sets the split. Keep them far apart, join them with a thin wire, and each sits at V = kq/R, so equal potentials give q ∝ R. A sphere of radius 5.0 cm carrying +14 nC, wired to a neutral sphere of radius 2.0 cm, ends at +10 nC while the small one takes +4.0 nC. Notice that the larger share went to the larger sphere, not to the one that started charged: the split is decided by radius alone. Watch what the electrons did — the big sphere fell from +14 nC to +10 nC, so 2.5 × 10¹⁰ electrons ran from the small neutral sphere onto it. Why both must reach one potential is proved in the unit on electric potential; the ratio is usable before then.

Charging by induction never touches the object being charged. Hold a rod at −6.0 nC beside a metal sphere on an insulating stand. Step one: the rod's field pushes the sphere's conduction electrons to the far side, leaving the near side short of them. The net charge is still zero, so nothing has been won yet. Step two: run a wire from the sphere to earth. The electrons crowded on the far side are now free to leave, and they go, because earth accepts them. Step three: remove the wire while the rod is still in place. The sphere is now short of electrons with no route back to earth. Step four: withdraw the rod, and the positive charge left behind spreads over the whole surface. The sphere is charged, its sign is opposite to the rod's, and the rod is untouched. Swap steps three and four and you get nothing: withdraw the rod first and the electrons simply climb back up the wire, leaving a neutral sphere. The sequence is the physics.

Earth is not a drain that empties things. It is a reservoir so large that charge entering or leaving it does not shift its potential. Which way charge moves through a grounding wire is decided by the field at the grounded object, never by the wire itself. A negative rod nearby drives electrons down into the earth and leaves the object positive; a positive rod draws electrons up out of the earth and leaves it negative. This is also why a grounded conductor sitting near a charge is not neutral. Grounding does not make the field inside the metal vanish — that is already true of any conductor in electrostatic equilibrium, charged or not. What the wire fixes is the potential: the conductor takes on exactly the charge that holds it at the earth's potential, and how much that is depends on the geometry. For a point charge q at distance d from the centre of a grounded sphere of radius R, the charge drawn from earth is −qR/d, a result the method of images will prove in a later unit. With q = −6.0 nC, R = 4.0 cm and d = 12 cm the sphere takes +2.0 nC, and at d = 24 cm only +1.0 nC. The nearer the inducing charge when you cut the wire, the more you keep.

Three questions in order settle the sign of every problem in this topic. Did the charged object touch the target? If it did, this is contact charging: the target ends with the same sign as the charger, and the charger itself ends with less charge than it started with. If it did not, was there a path to earth that was broken while the charged object was still present? If so, this is induction: the target ends with the opposite sign, the charger is unchanged, and the charge was traded with the earth. If neither, the target was only polarized, and it ends neutral however dramatic it looked while the rod was near. Run the four-step sequence above through these questions, at the 12 cm spacing used earlier, and the answers appear before any arithmetic — sphere +2.0 nC, rod still −6.0 nC, earth −2.0 nC, the three summing to −6.0 nC, which is what the system held before anything was done to it. When a calculation disagrees with that ledger, the calculation is wrong.

Four limits matter. Charge does not stay put: on a humid day a film of water on an insulator carries it away in seconds, which is why these demonstrations fail in August and work in January. There is also a hard ceiling, because a surface cannot exceed σₘₐₓ = ε₀E_b, and with E_b = 3.0 × 10⁶ V m⁻¹ for dry air that is 2.7 × 10⁻⁵ C m⁻²; a charged face of 1.0 × 10⁻² m² therefore carries at most 2.7 × 10⁻⁷ C, which is why these demonstrations deal in nanocoulombs. The triboelectric series is a rule of thumb rather than a law — its order shifts with roughness, contamination and humidity, and some pairs reverse outright. And the sharing results assume ideal conductors held far apart; two spheres in contact are close enough to distort each other's charge, so q ∝ R is a sound estimate rather than an exact answer. What survives all four is the bookkeeping: whatever leaves one object arrives somewhere else, in whole electrons.