All subjects · Physics · WPH14 (Unit 4)

Accelerating and detecting charged particles

Particle physics relies on producing beams of charged particles, accelerating them with electric fields, steering them with magnetic fields and detecting what comes out.

Thermionic emission

When a metal filament is heated, some electrons gain enough energy to escape from its surface: thermionic emission. In an electron gun, a p.d. V between the hot cathode and an anode accelerates them. Each electron gains kinetic energy eV = (1/2)mv² (for speeds much less than c).

Charged particles in a magnetic field

A charge moving at right angles to a uniform field B feels a force Bqv at right angles to its velocity, so it moves in a circle. Setting Bqv = mv² / r gives

r = p / BQ

Faster (higher momentum) particles move in larger circles; a stronger field or larger charge gives a tighter circle.

Linear accelerators and cyclotrons

Linac: a line of drift tubes connected to an alternating p.d. Particles are accelerated across each gap. The tubes get longer along the line because the particles go faster but must spend the same time (half a cycle) in each tube.
Cyclotron: two hollow D-shaped electrodes ('dees') in a magnetic field. The electric field across the gap accelerates the particles; the magnetic field bends them round to the gap again. As they speed up, their radius increases, so they spiral outwards. For non-relativistic speeds the time per half-turn stays the same, so a fixed-frequency alternating p.d. works.

Detectors

Charged particles ionise the material they pass through, leaving tracks (in bubble chambers, cloud chambers or electronic detectors). A magnetic field across the detector curves the tracks: the direction of curvature gives the sign of the charge, and the radius gives the momentum (r = p / BQ).

Worked example

Electrons are accelerated from rest through 1500 V. Find their speed.

E_k = eV = 1.60 x 10^-19 x 1500 = 2.40 x 10^-16 J
v = sqrt(2E_k / m) = sqrt(2 x 2.40 x 10^-16 / 9.11 x 10^-31)

Answer: v = 2.30 x 10⁷ m/s

Key idea: Heated filament releases electrons; eV = (1/2)mv²; r = p/BQ; electric fields accelerate, magnetic fields bend; tracks show charge and momentum.

Check yourself

Electrons are accelerated from rest through 400 V. Find the kinetic energy of each, in units of 10^-17 J.
Show answer
6.4 x 10^-17 J. E_k = eV = 1.60 x 10^-19 x 400 = 6.4 x 10^-17 J.
Find the speed of those electrons (accelerated through 400 V), in units of 10⁷ m/s, to 3 s.f.
Show answer
1.19 x 10⁷ m/s. v = sqrt(2 x 6.4 x 10^-17 / 9.11 x 10^-31) = 1.19 x 10⁷ m/s.
A proton with momentum 4.0 x 10^-20 kg m/s moves at right angles to a 0.50 T field. Find the radius of its path in m.
Show answer
0.5 m. r = p / BQ = 4.0 x 10^-20 / (0.50 x 1.60 x 10^-19) = 0.50 m.
A proton moves at 3.0 x 10⁶ m/s at right angles to a 0.20 T field. Find the radius of its path in m, to 3 s.f.
Show answer
0.157 m. p = 1.67 x 10^-27 x 3.0 x 10⁶ = 5.01 x 10^-21 kg m/s; r = 5.01 x 10^-21 / (0.20 x 1.60 x 10^-19) = 0.157 m.
What is thermionic emission?
- The emission of light from a hot gas
- The release of electrons when light hits a metal
- The release of electrons from a heated metal surface
- The decay of a nucleus by emitting an electron
Show answer
The release of electrons from a heated metal surface. Heating gives some electrons enough energy to escape the metal.
Why do the drift tubes in a linear accelerator get longer along its length?
- The particles move faster, but must spend the same time in each tube
- To make the particles slow down
- To increase the magnetic field
- So the particles can move in a circle
Show answer
The particles move faster, but must spend the same time in each tube. The p.d. alternates at a fixed frequency, so each tube must take half a cycle to cross.
What is the job of the magnetic field in a cyclotron?
- To accelerate the particles across the gap
- To slow the particles down
- To bend the particles round so they return to the gap
- To produce the particles
Show answer
To bend the particles round so they return to the gap. Only the electric field across the gap increases the speed; the magnetic force is perpendicular to the motion.
In a detector with a uniform magnetic field, one track curves much more tightly than another of the same charge. What does this tell you?
- It has a larger momentum
- It is neutral
- It has a larger charge
- It has a smaller momentum
Show answer
It has a smaller momentum. r = p / BQ, so a smaller radius means a smaller momentum.

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Last updated 7 November 2026. Spotted a mistake? Tell us.