Illustrated Physics
physics, drawn
Concept

Dielectric breakdown — where it appears

The sudden failure of an insulator when the electric field across it is strong enough for free electrons to multiply in avalanches and open a conducting path. Air breaks down at about three million volts per metre across gaps of millimetres, which is the field a spark marks.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The voltage a gas gap can hold, on one curve. The breakdown voltage of a gap in air between flat electrodes against the product of pressure and gap width, on logarithmic scales — Paschen's law, in which pressure and gap enter only as their product because both count how many collisions an electron makes on the way across. Townsend's model, with γ = 0.01 electrons freed per ion at the cathode, has its minimum of 305 V at 1.12 Pa·m — a gap of 11 μm at atmospheric pressure, or 112 Pa across a centimetre. Measured minima in air are about 330 V. To the left the gap is too short, or the gas too thin, for an electron to make enough collisions, and the voltage climbs steeply; below about 0.41 Pa·m there is no gas breakdown at any voltage. To the right, collisions are so frequent that an electron gains too little energy between them, and the voltage rises nearly in proportion to pd. Dashed, the empirical law for air at larger pd: 31.4 kV for a centimetre at one atmosphere, against the model's 35.5.

The spark that needs room to start

Air is an excellent insulator until it is not, and the usual statement of when — three megavolts a metre — is true only for gaps of about a centimetre. A gap breaks down when one electron's avalanche of ionisation sends back enough ions to the cathode to free one more electron, and that condition depends on the pressure and the gap only through their product. The result is a curve with a floor: about 330 volts in air, below which no gap of any width will spark, and above which both a thinner gas and a denser one insulate better.

electromagnetism · Dielectrics Water drops that charge two cans to a spark. The voltage between the two cans of a Kelvin water dropper against time, on a logarithmic axis, starting from a stray difference of 1 V, for 10, 20, 40 drops a second in each stream; drops 3 mm across, each with a capacitance of 0.17 pF to its ring, cans of 20 pF. Each drop carries a charge induced by the opposite can's potential into its own can, which raises the opposite can's induced charge on the next drop: the difference grows exponentially, multiplying by e every 6.0 s at 20 drops a second. It passes the 10 kV that will jump a few millimetres of air after 55 s — from one volt to a spark, with nothing but falling water.

The water drops that charge themselves to a spark

Two streams of water drip from one earthed pipe through two metal rings into two metal cans, and each ring is wired to the opposite can. Nothing is charged to begin with, nothing is rubbed, nothing is plugged in. Within a minute a spark cracks between the cans at ten thousand volts. A stray volt between them makes the drops forming in one ring pick up a slight charge, which they carry to the can that makes the other ring's drops pick up the opposite charge — a loop in which every drop strengthens the imbalance that charged it. Kelvin built it in 1867; it is a dynamo made of water and gravity.

electromagnetism · Potential

Named alongside it

The objects these essays reach for when they reach for this one.

CapacitanceElectric fieldElectric potentialElectrostatic inductionExponential growthIonisationMean free pathPaschen lawPositive feedbackSecondary emissionSimilarity lawSymmetry breaking

All concepts