Illustrated Physics
physics, drawn
Concept

Radiation resistance — where it appears

The part of a circuit's or antenna's effective resistance that accounts for power carried away as electromagnetic waves rather than turned into heat. For a small loop it grows as the square of the loop's area divided by the fourth power of the wavelength, which is why small circuits radiate so little.

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

Three terms, and one distance. The three terms of an oscillating dipole's electric field against distance, in units of a reciprocal wavenumber, both logarithmic. They fall as 1/u³, 1/u² and 1/u, so they are all equal at u = 1 — a distance of λ/2π, which is a property of the frequency and of nothing about the antenna. The heavy curve is the field the three actually add up to, and it is not their sum: the static and radiation terms are in antiphase and partly cancel, which is why the total dips below every one of them just inside the crossing before settling onto the 1/u the far field is made of.

The distance where a field changes its mind

An oscillating source has three fields around it, falling as the inverse cube, the inverse square and the inverse first power of distance. They are all equal at one radius, and that radius is the wavelength over 2π — a number containing nothing about the source at all. Inside it a source mostly stores energy; outside it, mostly loses it, and the two behaviours are different technologies rather than different strengths.

electromagnetism · Retardation Where the energy of a charged capacitor goes. The energy stored in a 1 nF capacitor charged to 10 V, in an identical empty one connected to it through a 100 Ω resistance, and dissipated as heat, as fractions of the starting energy, against time in units of the time constant RC/2 (50 ns here). Charge flows until both capacitors sit at 5 V. Each then holds a quarter of the original energy, and the other half has gone into the resistance, 86 per cent of it within the first time constant. The stored total (dashed) falls to one half and stays there.

The half a wire always takes

Charge a capacitor, connect it to an identical empty one, and wait. Charge flows until both sit at half the voltage, and when it stops, the two together hold exactly half the energy the first one started with. The other half has gone, and it has gone whatever the wire was made of: a thick copper bar and a megohm resistor take the same half, one in picoseconds and the other in milliseconds. Remove the resistance altogether and the energy still goes, as radio waves. The loss is not a property of the wire. It is what sharing a conserved quantity between two quadratic stores always costs.

electromagnetism · Field energy

Named alongside it

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

Adiabatic chargingCapacitorConservation of chargeDipole radiationElectromagnetic waveField energyImpedance matchingInelastic collisionThe inverse-square lawJoule heatingLc circuitNear field

All concepts