Thomson's e/m Experiment

Thomson used crossed electric and magnetic fields to select electrons with a specific velocity, where the electric and magnetic forces balanced. Only electrons with speed equal to E/B passed through and struck a fluorescent screen. By measuring the field strengths and analyzing the electron trajectories, Thomson calculated the charge-to-mass ratio as 1.759 × 10¹¹ coulombs per kilogram, revealing electrons as fundamental particles in all matter.

A velocity selector uses perpendicular electric and magnetic fields to isolate particles with a particular speed. When a charged particle enters, the magnetic force and electric force act in opposite directions. For a specific velocity, these forces balance exactly, allowing only those particles to pass straight through. Particles with different speeds experience a net force and are deflected away from the beam path.

Electrons are accelerated from a hot cathode through a potential difference between the cathode and anodes. The kinetic energy gained by the electrons equals the electric potential energy lost during acceleration. This relationship allows Thomson to calculate the electrons' velocity from the known accelerating voltage, providing a precise measurement needed for the charge-to-mass ratio calculation.

Thomson's measurements showed that the charge-to-mass ratio remained constant regardless of cathode material, residual gas in the tube, or other experimental variables. This independence demonstrated that the particles in the electron beam were fundamental constituents of all matter, not artifacts of specific experimental conditions. This discovery established the electron as the first truly elementary particle.

The fluorescent screen detected where velocity-selected electrons struck after passing through the crossed electric and magnetic fields. The glow at the impact point confirmed that only electrons with the correct speed E/B traveled straight through without deflection. This visual confirmation allowed Thomson to identify which particles satisfied the velocity selection condition and contributed to his measurements.

Fifteen years after Thomson's experiment, Robert Millikan precisely measured the electron's charge using the oil drop method. Combined with Thomson's charge-to-mass ratio, Millikan's charge measurement allowed scientists to calculate the electron's mass. This two-step approach provided complete characterization of the electron's fundamental properties and validated Thomson's groundbreaking discovery.

The electric and magnetic fields must be perpendicular to each other and both perpendicular to the particle's motion. The field strengths must satisfy the condition that the magnetic force equals the electric force for the desired velocity. When these geometric and force-balance conditions are met, only particles with speed v = E/B pass through undeflected, while all other speeds are filtered out.