Augmenting the fine beam tube: From hybrid measurements to magnetic field visualization
Oliver Bodensiek, Doerte Sonntag, Nils Wendorff, Georgia Albuquerque, Marcus Magnor
Augmenting the fine beam tube: From hybrid measurements to magnetic field visualization
O.Bodensiek, D.Sonntag, N.Wendorff, G.Albuquerque, and M.Magnor Institute for Science Education Research, Physics Group, Technische UniversitΓ€t Braunschweig Computer Graphics Lab, Technische UniversitΓ€t Braunschweig
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The Physics Teacher
57 (2019).
Since the emergence of Augmented Reality (AR), it has been a constant subject of educational research, as it can improve conceptual understanding and generally promote learning [1]. In addition, a motivational effect and improved interac-tion and collaboration through AR were observed [2]. Re-cently, AR technologies have taken a major leap forward in development, such that especially head-mounted devices or smartglasses came in question for supporting experimenta-tion in STEM education [3,4]. In line with these develop-ments, we here present an AR experiment in electrodynamics for undergraduate laboratory courses in physics using real-time physical data from and virtual tools on mobile devices to both analyze and visualize physical phenomena.
THEORETICAL
BACKGROUND
In order to determine the electron charge-to-mass ratio βπ/π π a fine beam tube is typically used in educational set-tings. Its main part is an electron gun that generates electrons by thermal glow emission, accelerates them due to a voltage π πππ between anode and cathode and bundles them into a fo-cused beam. The electron gun is embedded into an evacuated glass sphere back-filled with hydrogen or helium at low-pres-sure. Hence, the electron beam becomes visible due to impact ionization. This fine beam tube is mounted on a stand right in the middle of a Helmholtz coil pair, where a coil current πΌ ππππ generates an almost homogenous magnetic field. Provided πΌ ππππ is large enough compared to π πππ , the resulting Lorentz force deflects the electrons onto a circular path within the glass sphere. The Lorentz force acting on an electron with ve-locity π£β π in a magnetic field π΅ββ is given by
πΉβ = βπ (π£β π Γ π΅ββ) . For an ideal homogenous magnetic field and the electron ve-locity being perpendicular to the magnetic field, the Lorentz force acts as radial force, that is, π π β π£ π2 π = βπ β π£ π β π΅ according to amount and with π representing the radius of the circular electron path. Using the relations between π£ π and π πππ respectively between π΅ and πΌ ππππ the essential propor-tionality in this experiment is given by β ππ π β π πππ π β πΌ ππππ2 . EXPERIMENTAL
SETUP
In the experiment students use the Microsoft HoloLens [5] as AR smartglasses both to record measurement data and to study the physics of charged particles in magnetic fields in a hybrid, i.e. digitally enhanced, lab environment. π πππ and πΌ ππππ are measured with multimeters and gath-ered by a USB-connected single board computer [cf. Fig. 1], which in turn establishes a wireless data link to the Ho-loLens. On the HoloLensβ semi-transparent display the real-time measurement data is presented as numerical values in real time [cf. Fig. 2]. In order to determine the radius of the electron beam, we have added a virtual ruler that can by ges-ture control both be moved in depth to the plane of the elec-tron beam and adjusted to the diameter of the circular beam path [cf. Fig. 2]. Fig. 1. Experimental setup of the fine beam tube with Helmholtz coils, power supplies and multimeters connected via USB with a single board computer (SBC).
Fig. 2. View through the smartglasses while using the virtual ruler.
All numerical values that are needed to calculate the charge-to-mass ratio are shown on the display of the smart-glasses. By βair tappingβ a single record button (out of the field of view in Fig. 2), all three values are automatically added to a CSV file that can be analysed after the experi-ment. Additional measurements are recorded either for differ-ent voltages and coil currents measuring the altered diameter again, or by adjusting π πππ and πΌ ππππ such that the diameter keeps constant. Especially in the latter case, a measurement series can be done both rather quickly and by a single stu-dent, if wanted or necessary. Fig. 3. Visualization of the magnetic field as vector plot. In addi-tion, the theoretically predicted electron beam is augmented.
In addition to the hybrid measurement possibility we im-plemented a visualization of the magnetic field [cf. Fig. 3] according to the current experimental parameters. The user can also overlay the corresponding theoretically predicted electron beam. All field and beam data is calculated in ad-vance by the finite-element method for a relevant parameter space of π πππ and πΌ ππππ with a sufficiently narrow parameter grid. In between these points on the grid the AR applications interpolates the pre-calculated field and beam data linearly and visualizes it on the smartglasses accordingly. Moreover, the relevant formulas for Lorentz force, field strength as function of πΌ ππππ and electron velocity as function of π πππ can be enabled as overlay to the experiment (not shown here). The parameter(s) currently being changed in the experiment are then highlighted by color in the formulas. EXPERIMENTAL
RESULTS
We recorded a series of N=18 measurements with con-stant radius but different acceleration voltages and coil cur-rents in the AR environment. As a mean value we obtained β π π π β = β(1.76 Β± 0.01) β 10 C β kg β1 , which is remark-ably close to the CODATA value [6] β1.758820024(11) β 10 C β kg β1 . In several manual measurement series, visu-ally reading off the values, we best reached an accuracy of only about 3%. We relate the improved accuracy in the AR environment to the following two factors: One the one hand, even the stabilized power and voltage supplies we used vary over time. As an effect, one or both values read off may dif-fer a little from the ones immediately after calibration to the constant radius. This error source is reduced in our AR meas-urement, where both values are recorded simultaneously right after calibration. On the other hand, visually reading off the diameter includes a parallax error, as the measuring device lies approximately 9 cm in front of the electron beam. This error can be reduced by using a mirror on the backside of the glass sphere but it is still not as accurate as the virtual ruler in our AR environment, which can be placed directly in the plane of the electron beam in the glass sphere. The only drawback we experienced in using the AR envi-ronment for this specific experiment is the need to adjust the light conditions so that both the weakly glowing electron beam is clearly visible through the darkening HoloLens and one can still see enough to operate the power supplies. CONCLUSION
We implemented an augmented lab experiment for the fine beam tube using AR smartglasses. All measurements in order to determine the specific charge can be recorded digi-tally in the AR environment. With this AR-based approach we observe several advantages: First, the measured values seem to be more accurate compared to reading them off visu-ally. Second, acquisition of measurement values is easy and quick and can easily be done alone. Finally and probably most important, the additional field visualization coupled to real-time data provides an immediate feedback to the stu-dentsβ experimental actions. In combination with correspond-ing mathematical formulas of a theoretical description in a single hybrid learning environment we expect this to foster understanding relationships between theory and experiment as found in comparable AR experiments [4] since it provides high temporal and spatial contiguity thereby avoiding a split-attention effect [7].
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