Illustrated Physics
physics, drawn
Concept

Stopping power — where it appears

The energy a charged particle loses per unit length of path as it crosses matter, mostly to the electrons of the atoms it passes. Bethe's formula gives it; it falls as one over the particle's speed squared, which concentrates the dose at the end of the track.

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

A charge going past, as the field it delivers. The electric field across the line of motion at a point a distance b from the path of a passing charge, against time in units of b/c, on a logarithmic field axis in units of q/4πε₀b², for Lorentz factors of 1.2, 3, 10, 30. The peak is γ times the Coulomb field at rest and the width at half height is 2.311 b/c at γ = 1.2, 0.542 b/c at γ = 3, 0.154 b/c at γ = 10, 0.0511 b/c at γ = 30: taller by γ and shorter by γ, so the area under each curve — the sideways impulse the passing charge delivers, 2q²/4πε₀bv — is the same for all of them to within the integration's precision. A fast charge's field arrives as a thin, intense flash.

The charge that passes as a flash of light

A charge at rest has a field that no change of frame can turn into light. A charge going past at nearly the speed of light delivers a field that is, for every practical purpose, a pulse of light anyway: thin, perpendicular to the motion, with its electric and magnetic parts equal and crossed. Enrico Fermi saw in 1924 that such a field could be counted as photons, and the Large Hadron Collider now collides lead nuclei's photons with each other.

relativity · Field transformation The share of its energy a particle can hand to one electron. The largest fraction of its kinetic energy a muon, a pion, a proton or an alpha particle can give a free electron in one collision, against its Lorentz factor γ, on logarithmic axes. A slow proton can give at most 0.22 per cent, 4m/M, which is why a proton slows down through tens of thousands of gentle collisions rather than a few hard ones. The share rises as γ grows and reaches a half at γ = 916 for a proton and 101 for a muon — near M/2m, where the electron's energy in the centre-of-momentum frame has grown comparable to the projectile's, so that the two meet as equals and a head-on reversal can hand the electron most of the energy.

The kick a fast particle can give an electron

A slow proton crossing matter can give any one electron at most a fifth of a per cent of its energy, because an electron struck head-on by something two thousand times heavier rebounds at no more than twice the heavier one's speed. That rule of thumb fails at relativistic speeds, and fails upward: the electron's speed is capped below light, but its energy is not, and the largest kick grows as the square of the projectile's Lorentz factor until, above a teraelectronvolt, one collision can take more than half of everything a proton carries.

relativity · Relativistic dynamics

Named alongside it

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

The Lorentz factorCentre of momentum frameDelta raysElastic collisionElectromagnetic fieldEquivalent photonsField invariantsFour-momentumFourier transformThe Lorentz transformationPhotonVelocity addition

All concepts