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LearnYPH11WPH14 · Unit 4: Further Mechanics, Fields and ParticlesNuclear and particle physicsParticle accelerators and detectors
Nuclear and particle physics · Subtopic 4 of 4

Particle Accelerators and Detectors

Accelerators give charged particles huge kinetic energies using electric fields. A linac uses drift tubes of increasing length with an alternating p.d.; a cyclotron bends particles in a magnetic field so they cross the same gap repeatedly. In a magnetic field, r=pBQr=\frac p{BQ}, so track curvature reveals momentum and charge. Collision energy can create new particles: ΔE=c2Δm\Delta E=c^2\Delta m.

Edexcel YPH11 WPH14≈ 40 minRevision 1 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Explain how a linac and a cyclotron accelerate particles.
  • Use r=pBQr=\frac p{BQ} and f=BQ2πmf=\frac{BQ}{2\pi m}.
  • Interpret tracks in detectors.
  • Use the electronvolt and ΔE=c2Δm\Delta E=c^2\Delta m.
Pause and think

Why do physicists need ever larger accelerators to study ever smaller things?

Section 2 of 14

Core idea

Start hereSmashing to see

To see something tiny you need a probe with a tiny wavelength, and that means huge momentum. To create a heavy new particle you need its whole rest energy. Accelerators give charged particles both, using nothing more than electric and magnetic fields.

The big idea

Electric fields speed particles up (E=QVE=QV); magnetic fields bend them (r=pBQr=\frac p{BQ}). Detectors read charge and momentum from how tracks curve.

1. Circular motion in a field

Radius and frequency
  1. BQv=mv2rBQv=\frac{mv^2}r
    Magnetic force provides centripetal force.
  2. r=mvBQ=pBQr=\frac{mv}{BQ}=\frac p{BQ}
    Rearrange.
  3. T=2πrv=2πmBQT=\frac{2\pi r}v=\frac{2\pi m}{BQ}
    Period: vv cancels.
  4. f=BQ2πmf=\frac{BQ}{2\pi m}
    Constant, so a fixed-frequency supply works.
At very high speeds mm effectively grows, so cyclotrons give way to synchrotrons.
Worked exampleProton in a field

Proton at 1.0×1071.0\times10^7 m s⁻¹ in 0.500.50 T.

Goal
rr.
Strategy
r=mvBQr=\frac{mv}{BQ}.
  1. mv=1.67×10−20mv=1.67\times10^{-20}
    Momentum.
  2. BQ=8.0×10−20BQ=8.0\times10^{-20}
    Denominator.
  3. r=0.21 mr=0.21\text{ m}
    Divide.
Answer0.210.21 m.
✓ CheckAn electron at the same speed would curve about 1800 times more tightly ✓.

2. Linacs and detectors

Linear accelerator

Accelerate in gaps, coast in tubes.

Key takeawayWhy tubes lengthen The supply reverses every half-period; faster particles must travel further in that same time.
TrickNeutral particles They leave no tracks; look for a V-shaped pair of tracks appearing from nowhere where one decayed.
Pause and think

Why collide two beams head-on rather than hit a fixed target?

Summary

  • E=QVE=QV; 11 eV =1.6×10−19=1.6\times10^{-19} J.
  • r=pBQr=\frac p{BQ}.
  • f=BQ2πmf=\frac{BQ}{2\pi m}.
Key words
Linac
Straight accelerator with drift tubes.
Cyclotron
Circular accelerator with two dees in a magnetic field.
Electronvolt
Energy gained by e through 1 V.
HistoryLawrence’s cyclotron. Ernest Lawrence built the first cyclotron in 1931; it was 11 cm across. CERN's Large Hadron Collider is 27 km around.
Fun factAccelerators in hospitals. Most of the world's accelerators aren't for research: thousands of linacs treat cancer with high-energy X-rays.
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