Illustrated Physics
physics, drawn
Concept

Dipole field — where it appears

The magnetic or electric field of a pair of opposite poles seen from far away, falling as the inverse cube of distance with a characteristic two-lobed shape. The Earth's magnetic field and a bar magnet's are dipolar to a good approximation, and so is the field of any small loop of current.

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

A line carved into the X-rays of a magnetised star. A model X-ray spectrum of the kind fitted to accreting pulsars, drawn as energy per logarithmic interval on a logarithmic scale: a hard continuum that bends over above about 25 keV, with the photons near the cyclotron energy removed by resonant scattering. Dashed, the same continuum without the field. The fundamental is placed at 38 keV, where lines of this kind are seen; thermal motion of the scattering electrons along the field at kT = 8 keV broadens it to a width of about 4.8 keV. The second harmonic falls at 73.0 keV, a little below twice the fundamental. Read through ħeB/m with the relativistic level spacing and the redshift of a 1.4 solar-mass, 12 km star, z = 0.24, the fundamental says the field where the line forms is 4.24 × 10⁸ T. The depths and widths here are illustrative, not fitted to a star.

The circling that comes in quanta

An electron circling a magnetic field radiates at the frequency of its circling, and classically that is all: a continuous glow at whatever energy the circling has. On a neutron star the field is a hundred million tesla, the quantum of circling is a hard X-ray, and an electron lifted one step up falls back in a quarter of a femtosecond. So every electron there sits on the bottom step, and the X-rays that match the step are scattered out of the beam. The gap they leave is a line, and its energy is the field.

astrophysics · Radiating charge The circle of electrons a wave can talk to. Electron velocities along and across the magnetic field, in units of c. Shaded: a horseshoe of 10 keV electrons (speed 0.195c), the shape a beam takes when it is driven down into a strengthening field, with the electrons moving up along the field missing. Curves: the electrons a wave travelling across the field can exchange energy with, for wave frequencies of 0.995, 0.980, 0.960 times the cyclotron frequency. Because a faster electron is heavier and circles more slowly, at Ω/γ, each resonance is a semicircle of radius c√(1 − ω²/Ω²): 0.100, 0.199, 0.280c. A wave at 0.981Ω resonates with the horseshoe's middle.

The radio that only heavier electrons can make

Above every aurora the Earth broadcasts a gigawatt of radio that no one on the ground can hear. It comes out just below the frequency at which electrons circle the field there, and it is a maser — amplified by the electrons themselves. The surprise is what makes the amplifier work. Without relativity it could not: summed over every electron, a wave at the circling frequency is always absorbed. The few per cent by which a fast electron is heavier, and circles more slowly, is not a correction to the mechanism. It is the mechanism.

astrophysics · Radiating charge

Named alongside it

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

Cyclotron frequencyCyclotron motionGravitational redshiftLandau dampingLandau levelsMagnetic fieldMagnetosphereNeutron starPopulation inversionRadiating chargeRelativistic massResonant scattering

All concepts