Chapter 1 · Electrostatics: charge, force and sparks
Static electricity and charge
Where static comes from
The scene opens on a piece of amber and a wool cloth. The Greek word for amber is elektron, and ancient writers credit Thales of Miletus, around 600 BC, with noticing that rubbed amber picks up feathers. Today we know why. Atoms hold positive protons and negative electrons. Rubbing drags some electrons from one material onto the other, so one ends up slightly negative and the other slightly positive. Charge is measured in coulombs, and one electron carries 1.602 × 10⁻¹⁹ C. A balloon holding 10 nC (10⁻⁸ C) of extra charge has gained about 10⁻⁸ / 1.602 × 10⁻¹⁹ ≈ 6.2 × 10¹⁰ electrons.
Push and pull
Now two charged balloons hang from threads. Two negative ones swing apart; a negative and a positive one swing together. Like charges repel and unlike charges attract. In 1785 Charles-Augustin de Coulomb measured the force with a delicate torsion balance and found the law F = k·q₁·q₂ / r². F is the force in newtons, q₁ and q₂ are the charges in coulombs, r is the distance between them in metres, and k = 8.99 × 10⁹ N·m²/C². Because r is squared, twice the distance means a quarter of the force.
A worked example
Take two charges of 1 µC (10⁻⁶ C) each, 0.10 m apart. F = 8.99 × 10⁹ × 10⁻⁶ × 10⁻⁶ / 0.10² = 8.99 × 10⁻³ / 0.01 ≈ 0.90 N, close to the weight of a 90-gram apple. Move them to 0.20 m and the force drops to about 0.22 N. When the signs match, the arrows in the scene point apart; when they differ, the arrows point together. Use the sandbox under the picture to set both charges and the distance and read the force yourself.
Franklin, the kite and the rod
Clouds gather over a small house. In 1752 Benjamin Franklin proposed that lightning is electricity. The famous story says he flew a kite in a thunderstorm near Philadelphia; historians still debate exactly what he did, and some doubt that he did it at all. At least one experimenter who copied such work, Georg Richmann in St Petersburg in 1753, was killed. Never try it. Franklin's lasting idea was the lightning rod: a pointed metal rod joined to the ground by a thick cable gives lightning an easy path that avoids the building.
Counting the thunder
Light arrives almost at once, while sound travels at about 343 m/s. Count the seconds between a flash and its thunder and multiply by 343. If you count 6 s, the strike is 6 × 343 = 2,058 m away, roughly 2 km. A lightning flash carries currents of tens of thousands of amperes, far more than any household wire. So when thunder is audible, the safe place is indoors, away from windows, plugs and water. The rod in the scene is a safe path for the building; it does not make standing outside safe for you.
Conductors and insulators
In a copper wire each atom lets go of an outer electron that wanders freely, so charge flows easily. In glass, rubber and dry plastic the electrons stay bound to their atoms, so charge stays where it was put. The resistivity of copper is about 1.7 × 10⁻⁸ ohm-metres, while glass is at least 10¹⁰, more than 10¹⁷ times larger. That is why a cable is metal wrapped in plastic: the metal carries the charge and the plastic keeps it in. In the scene a metal ball spreads its charge over the whole surface in a flash, while a glass rod keeps its charge on one patch.
Hair on end
The scene ends with a Van de Graaff generator. A moving rubber belt carries charge up into a hollow metal dome, where it spreads over the outside. Robert Van de Graaff built the first one in 1929, and big machines reach millions of volts. Someone resting a hand on the dome, standing on an insulating stool, collects charge, and every hair carries the same sign, so the strands repel and spread out. Air breaks down at about 3 × 10⁶ V/m, so a 1 cm spark needs about 30,000 V. The charge is tiny, so the shock is mild, but use such a machine only in a supervised lesson.
In numbers
- 1.602 × 10⁻¹⁹ C
- the charge of a single electron
- 1785
- Coulomb publishes the law F = k·q₁q₂/r²
- 30,000 V
- needed for a spark to jump about 1 cm of air