The e/m experiment: student investigation into systematic uncertainties

In this work, we convert a common verification lab in the physics curriculum, measuring the charge-to-mass ratio of the electron (e/m), into an investigative lab on systematic uncertainty. The measurement apparatus can have systematic uncertainties resulting in values with significant discrepancy with the accepted value. Students were asked to quantify possible systematic uncertainties in the apparatus and correct them. Building upon each other’s work from semester to semester, students characterized four sources of systematic uncertainty in the apparatus independently of one another: (1) the current-to-magnetic field conversion factor of a Helmholtz coil, (2) the presence of external magnetic fields, (3) an offset in the internal ruler of the apparatus, and (4) a reduction in the accelerating voltage as compared to the applied voltage. Prior to accounting for these systematic uncertainties, the measured value of e/m was (2.03 ± 0.03)∗10¹¹ C/kg with a 15% discrepancy with the accepted value. After accounting for the systematic uncertainties, e/m was corrected to (1.751 ± 0.007)∗10¹¹ C/kg with a discrepancy of 0.5% with the accepted value. The precision of measurements was increased by a factor of four. This presentation describes the scientific approach developed by the students to untangle the sources of systematic uncertainty and correct e/m.