Illustrated Physics
physics, drawn
Concept

Susceptibility — where it appears

The ratio of the polarisation or magnetisation a material acquires to the field applied to it, which is how strongly it responds. Its reciprocal is linear in temperature for a paramagnet, and the slope of that line returns the magnetic moment of an ion.

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

The field a polarised sphere makes inside itself. A uniformly polarised sphere, its bound surface charge drawn at the size the cosine gives it, the uniform field that charge makes inside, and the exact dipole field it makes outside. The internal field is the same everywhere and points against the polarisation — that is what makes it a depolarising field — and its size is P/3ε₀, the third being the sphere's share of the one unit the three axes divide between them.

The field the matter takes away

Put a piece of glass in an electric field and the field inside it is smaller. How much smaller is not a property of glass. A needle of it keeps almost the whole field, a sphere keeps three-quarters, a slab across the field keeps a seventh — same material, same applied field, three answers, and the difference is arithmetic about shape.

electromagnetism · Dielectrics The field a classical partition function cannot see. The momentum plane of one classical charge, in units of the root-mean-square thermal momentum. With no field the Boltzmann weight is a set of circles about the origin; with a field the same circles sit about p = qA, displaced and otherwise unaltered, because the energy depends on p only through p − qA. Integrating over the whole plane therefore cannot notice the displacement, and the numbers beside the drawing are that integral evaluated at 6 displacements: the largest departure from the zero-field value is 3.3e-16, which is the precision of the arithmetic and not a physical effect. The classical free energy has no B in it, so the classical magnetisation is exactly zero at every field and every temperature — no paramagnetism, no diamagnetism, no ferromagnetism. Every magnetic material is therefore evidence of something classical mechanics does not contain.

The magnetism classical physics forbids

Write down the partition function of any collection of classical charges in a magnetic field, and the field cancels out. Not approximately, not to leading order — the integral is over all of momentum space and the field only shifts where the middle of it is. So classical statistical mechanics predicts no paramagnetism, no diamagnetism and no ferromagnetism, and a compass needle is a quantum instrument.

electromagnetism · Magnetisation Water's permittivity across six decades of frequency. The real and imaginary parts of water's permittivity against frequency, on logarithmic axes, from 10 to 16 in powers of ten hertz. ε′ begins at 80.1 — the number a textbook prints — falls through the Debye relaxation near twenty gigahertz, is dragged down again by the librational, bending and stretching bands of the molecule, and settles at 1.777 in the visible, whose square root is 1.3330: water's refractive index. The identity n = √ε_r is exact and is an identity between two numbers taken at the same frequency; using the static permittivity in it predicts an index of 8.9 and is the most instructive wrong answer in the subject. The curve is a Debye term and four Lorentz oscillators, with two parameters solved so that the two plateaus are the measured ones rather than fitted by eye.

The constant that depends on how fast it is asked

Water's relative permittivity is 80.1. Its refractive index is 1.333, and the square of 1.333 is 1.777. The identity n = √ε_r is exact, the two numbers differ by a factor of forty-five, and nothing is wrong with either — because a permittivity is a function of frequency and the two measurements were made eight orders of magnitude apart.

electromagnetism · Dielectrics

Named alongside it

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

DielectricPermittivityPolarisationAbsorptionAngular momentumBohr magnetonThe Boltzmann factorBound chargeBoundary conditionsCapacitanceCausalityConductors

All concepts