Electron charge-to-mass quotient

Thomson never measured the electron's charge or its mass; he measured this ratio, by balancing electric and magnetic deflection of a cathode-ray beam. The number came out about 1800 times larger than the corresponding ratio for a hydrogen ion, and since nobody believed charge could be that large, the particle had to be that light: the first subatomic particle, found by a ratio.

It remains the working constant of beam physics. A cyclotron frequency is f = (e/m)B/2π, so electrons gyrate at 28 GHz per tesla, which is why electron spin resonance runs at microwave frequencies while proton NMR sits at 42.6 MHz/T. The same ratio sets the deflection sensitivity of a CRT, the resolution of a mass spectrometer, and the Larmor radius of electrons in a tokamak or in the Earth's magnetosphere. The sign is negative by convention because the electron's charge is −e.