Experiment overview and relevant physics
In my Experimental Physics course, my lab partner, Bennett Bartel, and I decided to rediscover the electron charge to mass ratio. This is accomplished by measuring the trajectory of electrons in a magnetic field using a Uchida device called the TG-13. This experiment apparatus houses an electron gun in a vacuum with trace amounts of helium gas and has a Helmholtz electromagnetic coil geometry that produces a relatively uniform magnetic field at the electron gun region. When activating the electron gun, the beam forms a visible line, and activating the coils forces the beam to form a curved path in accordance with the Lorentz force.
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The TG-13 has a dial to increase the coil current, which increases the field strength and bends the trajectory of the electron beam more. By relating the Lorentz force to the centrifugal force required to form a circular path and relating the potential across the voltage gun and kinetic energy of a single electron, we can solve for the charge to mass ratio of an electron.
Analysis
We first looked at preliminary results. The diameter measured vs current in the Helmholtz coils has a relationship that is consistent with our model. Higher current in the the coil means stronger magnetic field (Biot-Savart Law) which means we should expect a smaller radius (which is directly proportional to the diameter).
In order to obtain our result, we plotted the data such that the curve's slope represents the charge to mass ratio. By applying a curve fit and retrieving the fit's slope, we arrive at the result. To verify that our result is within reason considering where error can accumulate in obtaining our data, we created a residuals plot.
Results
We measured the charge to mass ratio of an electron within 99.31% ± 1.21% of the accepted value.
Keeping an OSF lab journal
Documentation of any procedure is a useful practice not just for others' understanding, but also for our future selves. It was a requirement that my lab partner and I keep a lab journal for all of the experiments we've completed in this Experimental physics course. The structure we've settled on includes 4 sections, prelab, lab, analysis, and results and summary. The prelab section highlights the context of the experiment, goals, equipment required, expected procedure and expected behavior and predictions of the experiment's outcome. The lab section is a detailed step-by-step process of the data collection procedure. The analysis section, similar to lab, is a detailed process of what was required that we do with the data in order to analyze and obtain results. The results and summary section includes a summary of the experiment procedure and analysis procedure, a section delivering the results and a section interpreting the results and reflecting on the experiment and what improvements could be made. All of this documentation, as well as the data we collected and code we wrote for analysis, is shared in the form of an open science framework (OSF) project.
Reflection
Setting up this experiment without instructions and minimal guidance from the instructor was a profound experience for me. By only knowing the physics of the system, and obtaining the required equipment, we were able to conclude accurate results from our own data in an experiment led by ourselves. The process of determining what data to collect, what ways to streamline the steps, be the most accurate and consistent, then turn the data into results felt rewarding and satisfying. Additionally, I was fascinated to find out for myself the properties of a universal particle, the electron. This experiment is in my portfolio because I use physics concepts that I've learned in previous classes to arrive at tangible results.
My key takeaways from this experiment
- This experiment is in my portfolio because it displays my ability to set up an experiment with multiple measurable parameters, understand the relevant physics, analyze my data to arrive at a result, and document the process.
- The relevant physics used is the Lorentz force, centripetal force for circular motion, and kinetic energy.