Illustrated Physics
physics, drawn
Concept

Dynamo — where it appears

A conductor in motion that generates the magnetic field it moves through, sustaining the field against the resistive decay that would otherwise remove it. Above a threshold of speed the field grows from any seed; planetary cores, stars and self-excited generators are dynamos, and both directions of the field are equally possible.

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

The ring where an axisymmetric field vanishes. Field lines of the slowest-decaying dipole field of a conducting sphere, drawn in a plane through its axis (the axis is the left edge, the sphere's surface the arc). Each line is a contour of the flux function, which is zero on the axis and at infinity and positive between, so it must have a maximum. Here the maximum is on the equator at 0.873 of the radius: there the lines shrink to a point, which in three dimensions is a ring round the axis on which the meridional field is exactly zero. 7 of the 11 drawn lines leave the sphere and close outside; the other 4 close inside, round the ring. The toroidal current that makes the field is not zero on the ring: it is 89 per cent of its largest value.

The field no symmetric flow can keep

The Earth's core would forget its magnetic field in about forty thousand years, and the field is at least three and a half thousand million years old, so something must be making it again all the time. The obvious candidate is the flow of liquid iron. In 1934 Thomas Cowling proved that the simplest version cannot work: no motion of a conductor, however fast or however arranged, can keep up a field that is symmetric about an axis. The reason is a single ring inside the field where the current it needs cannot be driven.

astrophysics · Flux freezing A disc that makes its own field once it turns fast enough. A self-exciting disc dynamo started from rest, its motor's torque set so that, with no current, the disc would run at 0.8, 1.5, 2.5 times the critical speed R/M. Dashed: the disc's speed, in units of the critical speed. Solid: the current in its coil, in units of √(G/M), starting from a stray seed of a millionth, of either sign. Time is in units of the circuit's own L/R. At 0.8 the disc settles at its free-running speed, below critical, and the seed dies. Above it the disc spins up past the critical speed and nothing happens for a while — the current is growing exponentially from a millionth — until it reaches a tenth, at t ≈ 29 for 1.5 and 11 for 2.5 and becomes large enough to brake the disc. Speed and current then ring and settle at exactly the critical speed and a current of ±√(g − 1): 0.71 and 1.22, of the sign the seed happened to have.

The dynamo that reverses with nothing pushing it

A copper disc spinning in a magnetic field drives a current from its axle to its rim. Wire that current through a coil wound round the disc and the coil supplies the field the disc needs — and above one definite speed, a resistance divided by an inductance, the arrangement makes its own field out of any stray one, with nothing else magnetic anywhere. It cannot choose which way the field points; the stray field chooses. Couple two such discs, each feeding the other's coil, and with the motors' torque held perfectly steady the field flips direction again and again at intervals that follow no pattern. The simplest dynamo that works is also the simplest one that reverses.

astrophysics · Flux freezing

Named alongside it

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

InductionMagnetic fluxChaosConductivityDissipationFlux freezingGeomagnetic reversalHomopolar generatorMagnetic reynolds numberMean-field theoryResistivitySelf excitation

All concepts