Physics · Turning Points in Physics · A2 Level

Thomson's Measurement of the Specific Charge (e/m)

In 1897, J.J. Thomson passed a beam of cathode rays through a carefully balanced arrangement of electric and magnetic fields and, without ever weighing or counting a single particle, extracted a number that overturned the idea of the indivisible atom.

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Setting up the apparatus

Thomson's key experimental move was to pass a beam of cathode rays through a region containing both a uniform electric field and a uniform magnetic field, arranged so the two fields acted in opposite directions on the beam, then use the combined measurements to extract the ratio of the particles' charge to their mass — the specific charge, $e/m$ — without needing to know either quantity separately.

Inside an evacuated glass tube, cathode rays from a heated cathode (produced by thermionic emission, and accelerated by the tube's potential difference — see the previous lesson) passed through a small hole in an anode, producing a narrow, well-defined beam that continued in a straight line into a region between two parallel horizontal plates (producing a uniform electric field, deflecting the negative beam toward the positive plate) and between two magnetic coils (producing a uniform magnetic field, perpendicular to the electric field, deflecting the beam by the motor effect). Beyond this region, the beam struck a fluorescent screen marked with a scale, so the deflection of the beam could be read off directly as a spot of light.

Side-view schematic of Thomson's cathode ray tube. A heated cathode at the left emits a beam that passes through a hole in an anode, then travels rightward through a region between two horizontal parallel plates (electric field) that overlaps a region between two magnetic field coil symbols (magnetic field into or out of the page), before striking a fluorescent screen marked with a scale at the right. — Thomson's apparatus: a narrow beam of cathode rays passes through overlapping electric and magnetic fields before striking a calibrated fluorescent screen.

The velocity selector

The first stage of the experiment used the two fields together to find the speed of the particles in the beam, without needing to know their charge or mass.

DerivationThe velocity selector: v = E/B

With only the electric field switched on, the beam deflects toward the positive plate. Thomson then switched on the magnetic field as well, and adjusted its strength $B$ until the beam returned to travelling in a straight line, undeflected, striking the screen at the same point as with both fields off.

When the beam is undeflected, the electric and magnetic forces on each electron must be equal in size and opposite in direction — they exactly balance.

The electric force on a charge $e$ in a field of strength $E$ is $F_E = eE$. The magnetic force on a charge $e$ moving at speed $v$ perpendicular to a field of flux density $B$ is $F_B = Bev$.

Setting these equal for the balanced (undeflected) condition: $eE = Bev$.

The charge $e$ cancels from both sides, leaving $v = \dfrac{E}{B}$.

This is the crucial step: the speed of the particles in the beam can be found from the field strengths alone, with no need to know the particles' charge or mass at all. This arrangement — crossed electric and magnetic fields balanced to select a single speed — is now called a velocity selector, and is used wherever a beam of charged particles of known, uniform speed is needed.

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Finding e/m from the electric-only deflection

With the beam's speed $v$ known, Thomson then switched off the magnetic field, leaving only the electric field to deflect the beam, and measured the resulting deflection on the screen. This deflection depends on $e/m$: a particle with a larger charge feels a stronger electric force and deflects more; a particle with a larger mass has more inertia and deflects less. Measuring the deflection, together with the known plate length, plate separation, accelerating voltage and the now-known speed $v$, let Thomson calculate the specific charge directly.

DerivationFinding e/m from the electric deflection

With the magnetic field off, the electric force $F_E = eE$ is the only horizontal (deflecting) force on each electron as it crosses the plates, giving it a constant acceleration $a = \dfrac{eE}{m}$ perpendicular to its original direction of travel.

While crossing the plates (length $l$, at speed $v$ along the tube), the electron spends time $t = \dfrac{l}{v}$ in the field, and picks up a perpendicular deflection $y = \tfrac{1}{2}at^2 = \dfrac{1}{2}\cdot\dfrac{eE}{m}\cdot\left(\dfrac{l}{v}\right)^2$, by the standard constant-acceleration (suvat) equation for displacement.

Rearranging for the specific charge:

$\dfrac{e}{m} = \dfrac{2yv^2}{El^2}$

Every quantity on the right — the measured deflection $y$, the speed $v$ found from the velocity selector, the field strength $E$, and the plate length $l$ — is known from the apparatus, so $e/m$ can be calculated directly.

Thomson's result, refined over repeated measurements with different gases and different cathode materials, gave a specific charge of roughly $e/m \approx 1.76\times10^{11}\,\text{C}\,\text{kg}^{-1}$ — a figure consistent with the modern accepted value.

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Why not measure e and m separately?

Thomson's apparatus could only ever measure the ratio $e/m$, not $e$ and $m$ individually — deflection in the tube depends on both quantities together, and no combination of electric and magnetic measurements inside the tube alone can separate them. A particle with twice the charge and twice the mass would deflect by exactly the same amount as the original, so the tube genuinely cannot distinguish between them. Pinning down the charge $e$ itself required a completely different experiment, which is the subject of the next lesson: Millikan's oil-drop experiment.

Why the result mattered

Two features of Thomson's result were genuinely shocking to physicists in 1897.

First, the specific charge $e/m$ came out roughly 1800 times larger than the specific charge of a hydrogen ion (the lightest known charged particle at the time, from electrolysis measurements). Since nothing suggested the cathode ray particles carried an enormous charge, the natural conclusion was that their mass was roughly 1800 times smaller than a hydrogen atom's — meaning cathode rays were made of something far lighter than the lightest atom known.

Second, and just as important, Thomson found the same value of $e/m$ regardless of which gas filled the tube or which metal the cathode was made from. If cathode rays were fragments of whatever atoms happened to be in the tube, changing the gas or the cathode material should have changed the result. It didn't. This showed that cathode rays were not specific to any one element — they were a single, universal type of particle, present inside the atoms of every element tested. Thomson named this particle the electron, and proposed that it was a fundamental constituent of all atoms.

Overturning the indivisible atom

Before 1897, the atom was widely treated as the fundamental, indivisible building block of matter (the "billiard ball" model) — the word "atom" itself derives from the Greek for "uncuttable". Thomson's discovery that atoms contain even smaller, lighter, universal charged particles broke that model completely, and opened the question of what an atom's internal structure actually looks like — a question that runs through the rest of this module and into the core Nuclear & Particle Physics topic (Rutherford scattering, the nuclear atom, and the particles found since).

Key takeaways

Thomson passed a cathode ray beam through crossed (perpendicular) electric and magnetic fields, first balancing them so the beam travelled undeflected.
At balance, $eE = Bev$, so the particles' speed can be found from the field strengths alone: $v = E/B$ — a velocity selector.
Switching off the magnetic field and measuring the electric-only deflection $y$ gives $e/m = \dfrac{2yv^2}{El^2}$, using the known plate length $l$ and field strength $E$.
Thomson's apparatus measures only the ratio $e/m$, not $e$ and $m$ separately, because deflection depends on both together — finding $e$ itself needed a different experiment (Millikan's, next lesson).
The measured $e/m$ was about 1800 times larger than for the hydrogen ion, implying a particle far lighter than any atom.
The same value of $e/m$ was found regardless of the gas or cathode material used, showing the particle is a universal constituent of matter, not specific to one element.
This showed cathode ray particles — electrons — overturn the idea of the atom as an indivisible fundamental particle.

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Thermionic Emission

Millikan's Oil-Drop Experiment