Illustrated Physics
physics, drawn
Concept

Self-force — where it appears

The force a charge or mass exerts on itself through the field it radiates, the reaction that makes an accelerated charge lose energy. Its classical form, the Abraham–Lorentz force, predicts runaway solutions and is tamed only by treating radiation reaction as small.

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

The outward pull on a charged surface. Electrostatic pressure against the field at a conductor's surface. The quantity is ½ε₀E², the energy density of the field itself, and it is outward whatever the sign of the charge — like charges repel, and a charged surface is trying to fly apart. The factor of a half is the interesting part and is where a first attempt goes wrong: the field is σ/ε₀ outside and zero inside, and the layer of charge feels neither of those but their mean, because no charge exerts a force on itself. 0.5 MV/m gives 1.1 Pa, 1 MV/m gives 4.4 Pa, 2 MV/m gives 17.7 Pa, 3 MV/m gives 39.8 Pa, 5 MV/m gives 110.7 Pa. Those are small pressures — three megavolts per metre is the breakdown field of air and pulls with about a hundredth of an atmosphere — which is why electrostatic forces shape soap films and dust and not much that is stiffer, and why the same pressure set against surface tension has a definite size of drop at which it wins.

The pressure a charge puts on its own metal

Charge on a conductor sits on the surface and tries to leave. The outward pull is half epsilon-nought E squared, the half is because a charge exerts no force on itself, and setting that pull against surface tension gives the largest a charged drop is allowed to be — a number Rayleigh wrote down in 1882 and an industry now depends on.

electromagnetism · Conductors An electron that runs into light and loses its energy to it. The energy of an electron of 511 MeV (γ = 1000) as it passes head-on through a 10-cycle pulse of 0.8 µm light, as a fraction of its starting energy, against the number of laser cycles it has crossed, for normalised field strengths a₀ = 30 and 100: with radiation reaction (solid) and without (dashed). Without it, the electron is shaken sideways while in the light and leaves with exactly the energy it brought, as a plane wave requires. With it, each half-cycle near the pulse's peak radiates away a slice: the electron leaves with 76 per cent of its energy at a₀ = 30 and 22 per cent at a₀ = 100, the rest gone as gamma rays.

The light that takes back an electron's energy

An electron at rest in the most intense laser light ever made feels its own radiation as a force a millionth of the light's push — the textbook reason radiation reaction never matters. Send the electron into the light at nearly the speed of light and the arithmetic turns over. In its own frame the light is stronger by twice its Lorentz factor, the power it radiates grows as the square of that, and a pulse a few tens of femtoseconds long can strip it of most of its energy as gamma rays. That is where the classical theory of a radiating charge, argued over for a century, finally has to answer to experiment — and where it starts to fail for quantum reasons.

relativity · Relativistic dynamics

Named alongside it

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

Boundary conditionCompton scatteringConductorCritical fieldElectrosprayElectrostatic pressureEnergy densityInstabilityLaplace pressureLaserThe Lorentz factorPlane wave

All concepts