Electron Beams and Specific Charge

A large potential difference across a low-pressure discharge tube produces cathode rays travelling from the negative electrode. Electric and magnetic deflections show that the rays carry negative charge. Their properties did not depend on the gas or cathode material, suggesting a common constituent of matter rather than a different particle for every substance.

In an electron gun, heating a metal cathode gives some electrons enough energy to escape the surface: thermionic emission. The accelerating anode supplies an electric field that increases their kinetic energy. The heater releases electrons; the accelerating potential then controls their energy.

Send the beam perpendicular to a known approximately uniform magnetic field. Magnetic force supplies centripetal force: $evB=m_ev^2/r$. The magnetic field changes direction of motion, not speed, because its force is perpendicular to velocity.

Eliminate speed using the accelerating-energy equation. Measure V, B and the circular radius r; substitute in SI units. A radius is half the diameter seen on the screen. A field component parallel to motion does not supply the required circular force, so alignment matters.

Thomson’s electron specific-charge magnitude was much larger than that of a hydrogen ion, implying a much lighter particle if the charge magnitude was similar. Electron $e/m_e$ is about $1.76\times10^{11}$ C kg⁻¹, while proton $e/m_p$ is about $9.58\times10^7$ C kg⁻¹. Their ratio is about 1836.

A specific-charge measurement alone does not separately give charge and mass. Combining it with an independent charge measurement allows mass to be calculated. This is the link between Thomson’s experiment and Millikan’s later work.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.