Illustrated Physics
physics, drawn
Concept

Dipole — where it appears

The leading description of a neutral arrangement of charge or current that is not symmetric, being a separation times a magnitude. Its field falls one power faster than a monopole's, and it is the first term that survives when the total charge vanishes.

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

A force that points across the beam, not along it. The intensity of a beam focused to a waist of 0.5 µm, and the force it exerts on a 60 nm polystyrene sphere in water, across the beam. The force is not a pressure and does not point along the light: it is the pull on an induced dipole sitting in a non-uniform field, proportional to the gradient of the intensity rather than to the intensity, and it points up the gradient — towards the bright axis from either side. It vanishes exactly on the axis, which is what makes the axis a trap rather than a place. The well is 47 times kT deep at 100 milliwatts, which is why the particle stays: thermal motion explores it and does not escape it. The stiffness near the bottom is 3.070 piconewtons per micrometre, and a particle in a spring that stiff wanders 36 nanometres from centre.

The light that pulls rather than pushes

Radiation pressure is momentum arriving, and it points along the beam. A gradient of intensity does something else entirely — it polarises a particle and then pulls the induced dipole up the gradient — so a focused beam holds a particle at its waist against the push, and the force that does it is not a pressure at all.

astrophysics · Radiation pressure Two fields of the same magnet, and inside they point opposite ways. A uniformly magnetised sphere, with the field lines of B on the left and of H on the right, both computed from the exact solution — uniform inside, a dipole outside. Outside the sphere the two pictures are identical up to a constant, because there B is μ₀ times H and nothing else. Inside they are opposite: B is 0.67 tesla pointing along the magnetisation and H is 267 kiloamps a metre pointing against it. The B lines close on themselves and never end; the H lines begin on the top face and end on the bottom, which is what a field with sources looks like. Nothing about the magnet changed between the two panels — only which currents the circulation is allowed to count.

The field that points against the magnet it is in

There are two magnetic fields in use and the difference between them is which currents a loop is allowed to count. The consequence nobody expects on being told the definitions: inside a permanent magnet H points the other way from B. It has to — a loop inside the magnet threads no wire, so its H circulation is zero, and the only arrangement left has H running backwards.

electromagnetism · Ampere law

Named alongside it

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

Ampere lawBound chargeBoundary conditionsBrownian motionCalibrationConstitutive lawDemagnetising fieldEquipartitionFluxGradient forceMagnetic circuitMagnetic field

All concepts