DOI: 10.11648/j.innov.20260702.13 ISSN: 2994-7138

Experimental Determination of Electron-to-Charge Mass Ratio in Physics Laboratory

Shambel Admassie, Agumassie Addis
Show PDF Cite
The charge-to-mass ratio (e/m) of the electron is a fundamental physical constant essential for understanding the behavior of charged particles within electromagnetic fields and the development of atomic theory. This study details the experimental determination of the e/m ratio conducted at the Debre Markos University Physics Laboratory using a Helmholtz coil apparatus and a fine beam tube. The experiment's primary objective was to verify the theoretical relationship between an electron's circular trajectory, its accelerating potential, and the applied magnetic field strength. The research employed a dual-variable data acquisition strategy to ensure accuracy and reliability. In the first approach, the accelerating voltage was varied from 100 V to 190 V while maintaining constant coil currents between 2.00A and 2.50A. In the second approach, the coil current was varied between 1.01A and 1.9A while holding the accelerating voltage constant at intervals up to 199.8 V. By measuring the radius (r) of the visible electron beam, the study analyzed the linear relationship between the square of the radius (r 2 ) and the accelerating voltage (V), as well as the inverse square of the current (1/I 2 ). Linear regression analysis of the gathered data yielded high coefficients of determination (R 2 ), ranging from 0.9898 to 0.9978, with an average of approximately 0.993. These values confirm a strong agreement with the theoretical models derived from the Lorentz force and the work-energy theorem. The experimentally determined mean value for the e/m ratio was 1.7488 \times 10 11 C/kg. Compared to the internationally accepted value of 1.7588 \times 10 11 C/kg, the experiment produced an average percentage error of 2.75%. Minor discrepancies were attributed to systematic and random errors, such as parallax when reading the mirrored scale, the influence of the Earth’s magnetic field, and minor fluctuations in the DC power supply. Despite these limitations, the results demonstrate that the Helmholtz coil method provides a robust and reliable verification of the electron's intrinsic properties. The study concludes that the experimental setup effectively illustrates the principles of classical electromagnetism and particle dynamics.

More from our Archive