PHYSICS LAB
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ELECTRICITY & MAGNETISM · LAB 33

Cyclotron laboratory

Synchronise an alternating electric field with magnetic bending to accelerate particles along an expanding spiral.

PARTICLE STATEACCELERATING
ParticleTrajectoryMagnetic forceElectric forceExtracted beam
PARTICLEPROTON

q = +1e · m = 1

SPEED / RADIUS0.40 / 0.40

r = mv / |q|B

CYCLOTRON / RF1.00 / 1.00

mismatch 0.0%

GAP CROSSINGS0

0.0 completed orbits

BEAM ENERGY0.08 a.u.

phase 0° · in sync

HOW IT WORKS

Timed pushes, magnetic turns

  1. The magnetic field bends the particle into a semicircle.
  2. Each dee shields it from the electric field.
  3. The voltage reverses before it reaches the gap.
  4. Every correctly timed crossing increases its energy.
  5. Its increasing speed creates an expanding orbital radius.
  6. A deflector guides the beam to a target.
F = q(E + v × B)fc = |q|B / 2πmK = ½mv²

Safety: Real particle accelerators involve high voltage, strong magnetic fields, ionising radiation and vacuum systems requiring specialist facilities.