Illustrated Physics
physics, drawn
Concept

Magnetism — where it appears

The set of effects produced by moving charge, which the theory of relativity shows to be electrostatics viewed from another frame. The drift speed of electrons in a wire is a fraction of a millimetre a second, so the whole of magnetism is a length contraction of order 10⁻²⁵ acting on an enormous charge density.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

What a collapse does to a field. A body of radius 700,000 km carrying a field of 0.01 T, collapsing to 10 km. The flux through every comoving loop is fixed, so B goes as 1/R² and the field reaches 4.9·10⁷ T — a compression of 7·10⁴ in radius bought a factor of 4.9·10⁹ in field. The line has slope exactly −2 and that is the only claim being made: what a real object ends up with also depends on how well the flux was held, and on what generated it.

The field that cannot get out

Squeeze a lump of conducting fluid and its magnetic field comes with it, because the flux through any loop that moves with the material cannot change. Halve the radius and the field goes up fourfold; collapse by a factor of seventy thousand and it goes up by five thousand million.

astrophysics · Flux freezing The same wire, seen twice at 0.6c. Above: the wire in the laboratory. The lattice is at rest and the electrons drift, so the electrons are the contracted ones — and the wire is neutral, which means their contracted spacing is what the manufacture of a neutral wire produced. Below: the same wire seen by something moving with the electrons at 0.6c. Now the electrons are at rest and the spacing between them stretches by γ = 1.250, while the lattice moves and its spacing contracts by the same factor. The two densities no longer cancel and the wire is charged. Nothing was done to the wire; the only thing that changed is who is looking, and the magnetic force in the first frame is the electric force in the second.

Magnetism is electricity seen sideways

The force on a charge moving beside a current-carrying wire is magnetic in the laboratory and purely electrostatic in the charge's own frame. Both calculations give the same answer, and the drift speed that makes them agree corresponds to a Lorentz factor differing from one in the twenty-sixth decimal place.

relativity · Field transformation Where a magnet actually sits on its own curve. The second quadrant of a magnet's B–H curve, for a material with a remanence of 1.28 T, and the load lines four shapes of it impose. A magnet's own poles put it in a reverse field of N·M, so the working point is where the curve meets the line B = −μ₀(1−N)/N·H. A long thin magnet with N = 0.02 keeps 98 per cent of its remanence and a squat one with N = 0.7 keeps 30 per cent — the same material, cut differently.

The magnet that has to fight its own field

A bar magnet's own poles put it in a reverse field, so the same material cut short and fat is weak and cut long and thin is strong. And a magnetised material does not have a magnetisation — it has a magnetisation and a history, which is why the word for what it does is the Greek for coming late.

electromagnetism · Magnetisation What a boost can and cannot do to a field. The electric and magnetic magnitudes of three fields, plotted against each other as the observer is boosted from -0.98c to 0.98c across them. Each field slides along a hyperbola, because E² − c²B² does not change: the recomputed value drifts by at most 2.6e-15 over every point drawn. The diagonal is E = cB, and which side of it a field starts on is permanent. Below it there is a speed at which the electric field vanishes; above it, one at which the magnetic field does; on it, a wave that no observer can slow, dim or unbalance.

The field nobody can transform away

A wire's magnetic field is an electric field seen from the wrong frame, and a charged plate's electric field is a magnetic one seen the same way. Neither trick works on a light wave. Two combinations of E and B are the same for every observer, and which side of one line a field sits on is a fact nothing about the observer can alter.

relativity · Field transformation

Named alongside it

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

Field transformationFlux freezingRelativityAnisotropyCharge densityCoercivityConductorsConservation lawsDemagnetising fieldDissipationDomainsElectric field

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