Target Reviewers: Experimental Physicists, Vacuum Systems Engineers, and Science Historians.
Abstract:
This technical assessment recreates the foundational 1897 J.J. Thomson experiment to determine the charge-to-mass ratio ($e/m$) of the electron. The methodology utilizes a cold-cathode vacuum tube accelerated by a high-voltage DC potential (3.2 kV) situated within a uniform magnetic field generated by calibrated Helmholtz coils. By correlating the Lorentz force and centripetal acceleration with the kinetic energy derived from the accelerating potential, a mathematical model for $e/m$ is established. Due to the high energy of the electron beam, the experiment utilizes angular deflection measurements on a phosphorus-coated internal plate to estimate the orbital radius. Quantitative results demonstrate high fidelity to NIST standards, achieving a measured ratio between $1.55 \times 10^{11}$ and $2.16 \times 10^{11}$ C/kg.
Experimental Summary: Determining the Electron Charge-to-Mass Ratio
0:07 - Historical and Theoretical Objectives: The project aims to re-verify the $e/m$ ratio, a discovery that historically confirmed the existence of subatomic particles. The experiment relies on the synthesis of Newtonian mechanics and electromagnetism.
0:46 - Principles of Electron Manipulation: Electrons are accelerated through a potential difference ($V$) in a vacuum. Manipulation is achieved via electric or magnetic fields. A magnetic field ($B$) perpendicular to the electron velocity ($v$) exerts a force ($F = evB$).
2:07 - Derivation of the Master Equation: By equating the magnetic Lorentz force to the centripetal force ($mv^2/r$) and integrating the conservation of energy ($eV = 1/2 mv^2$), the ratio is isolated: $e/m = 2V / (B^2 r^2)$.
6:00 - Apparatus Specifications: The system employs Helmholtz coils designed with a radius ($R$) equal to their separation distance to ensure a uniform magnetic field in the center. A vacuum tube is placed at the center of this field.
10:21 - Vacuum Tube Mechanics: Due to the failure of a thermionic emission tube, a cold-cathode tube is utilized. This requires higher potentials (~3,000V) to initiate field emission. Visualization of the beam is achieved by electrons striking a phosphorus-painted internal plate, emitting photons.
14:23 - Helmholtz Coil Calibration: The magnetic flux density ($B$) is verified using a Hall effect sensor and a Gauss meter. The experimental measurement of $7.8 \times 10^{-4}$ Tesla per Ampere aligns with the theoretical equation within a few percentage points of error.
21:09 - Data Consistency Checks: Magnetic field strength is shown to be linear with current (doubling current from 1A to 2A doubles the Tesla reading). Neodymium magnets are used for far-field comparison, showing significantly higher but non-uniform flux density (0.57 Tesla) compared to the coil's uniform field.
23:04 - Experimental Deflection Measurement: The beam is accelerated at 3,200V. Deflection is measured at $\pm 0.5$ Amps of coil current. The beam exhibits an angular deflection of approximately $6.5^\circ$. Observations confirm that increasing voltage (energy) decreases deflection, as predicted by the larger theoretical radius ($r$).
27:46 - Quantitative Results and Accuracy: By converting the $6.5^\circ$ deflection over a 50mm path into an effective radius, the $e/m$ ratio is calculated at approximately $1.75 \times 10^{11}$ C/kg. This result is in direct agreement with the NIST established value.
29:52 - Historical Synthesis: The experiment acknowledges J.J. Thomson’s 1897 discovery of the ratio and Robert Millikan’s subsequent oil-drop experiment (1909). Millikan's determination of the elementary charge ($e \approx 1.6 \times 10^{-19}$ C) allows the calculation of the electron's mass ($m \approx 9.1 \times 10^{-31}$ kg).
33:42 - Logistics and Giveaway: The episode concludes with the announcement of two Siglent SDS1104X HD oscilloscope winners, supported by Patreon and industry donation.