Magnetic fields produced by electric railways
MMagnetic fields produced by electric railways
Martín Monteiro(a), Giovanni Organtini(b),and Arturo C. Marti(c),(a) Universidad ORT Uruguay; [email protected](b) Universida di Roma La Sapienza, Italy, [email protected](c) Universidad de la República, Uruguay, [email protected]
We propose a simple experiment to explore magnetic fields created by electric railways and comparethem with a simple model and parameters estimated using easily available information. A pedestrianwalking on an overpass above train tracks registers the components of the magnetic field with the built-inmagnetometer of a smartphone. The experimental results are successfully compared with a model of themagnetic field of the transmission lines and the local Earth’s magnetic field. This experiment, suitable fora field trip, involves several abilities, such as modeling the magnetic field of power lines, looking upreliable information and estimating non-easily accessible quantities.
Electromagnetic fields.
We live surrounded by electromagnetic fields covering all ranges of spatial andtemporal scales. Most of them are difficult to measure or even to detect. Notable exceptions are static orquasi-static magnetic fields which can be detected or measured with a compass or a with smartphonesensor. In the past, smartphone experiments were proposed using small currents [1-3], magnets [4,5], andthe Earth magnetic field [6]. The other example, not so obvious, consists of the magnetic fields producedby power electric currents. Most of the power systems are alternating current (AC), 50 Hz or 60 Hz and,as a consequence, the created magnetic field results difficult to measure. However, some railways systemsare powered by direct currents (DC) and thus the magnetic field produced by overhead lines (also knownas catenaries) can be occasionally measured. In this work, we propose the analysis of the magnetic fieldproduced by an electric train near Rome.
The experiment.
Modern smartphones usually possesses built-in magnetometer that have been employedin several physics experiments [1-6].
The experiment proposed here was performed outdoors in a peacefulplace near Rome. A pedestrian walking on an overpass (shown in Fig. 1) above the tracks of the railwaysregisters the magnetic field with her/his smartphone. At that moment, no train was in the vicinity and noother vehicle was passing by. While the experimenter was walking at nearly constant speed (~ 1 m/s) thesmartphone was held horizontally with the screen orientated upwards. This procedure is similar to the“fly-by” on an air track proposed in [3]. Thanks to the Phyphox app [7] the three components of themagnetic field were registered as the pedestrian walked over the bridge.
The comparison.
To propose a simple model we calculated the magnetic field by means of the Biot-Savart law with the DC currents and distances sketched in Fig. 2. According to the train company thepower of the engines is 2.2 kW and the voltage of the lines is 3kV (DC), resulting an intensity ofapproximately I = 733 A, though this value can vary depending on the number of convoys nearby andtheir accelerations. We assume a current in one direction through the catenary and the opposite, returning,current uniformly distributed in the two tracks. The comparison of the field measurements and the model is displayed in Fig. 3. The left panel shows thecomponents of the magnetic field as a function of the position along a horizontal line, perpendicular to thecatenary. The reference frame is chosen to be the same of the smartphone, in which the x-axis is parallelto the tracks, the y-axis is perpendicular to them and parallel to the overpass, while the z-axis is vertical.The right panel shows the magnetic field as the sum of that of the catenary, the tracks and the Earth. FromNOAA’s geomagnetic calculator for that location, the components of Earth’s magnetic field wereobtained. In particular, vertical component, horizontal component and declination (the angle between theorizontal magnetic field and the geographic north). The orientation of the tracks, the path and the Earth’smagnetic field were obtained from the satellite view. From the above, the components x, y, z (in thephone’s reference system) of the earth's magnetic field were determined.
Systematic effects . The absolute value of the magnetic field measured by most smartphones is quiteprecise, but not as accurate [8]. Since it is used as a tool for navigation, the magnetometer is oftencalibrated assuming the intensity of the magnetic field to be of the order of 50 μT. From the point of viewof this experiment, such an effect is not relevant, but it is worth knowing it. On the contrary, sensitivity isenough to seamlessly measure the magnetic field produced by a current of the order of 1 A at few cm, thatcan be obtained with a common battery connected to the ends of a long wire. The current flowing on atrain line may not be constant. The measurement, then, must not last too much to avoid spotting suddenchanges in the current. Moreover, both the ferromagnetic metal of which wagons are made, as well asthose of which cars are made, modify the magnetic field shape and intensity, such that the measurementcan be greatly affected if cars pass nearby or when the train is passing below the overpass. To perform themeasurements described in this paper it is then essential to choose a relatively quiet place. On the otherhand, it may be interesting to observe how the magnetic field changes when cars or wagons pass close tothe smartphone (e.g. standing on the platform when a train approaches).
Conclusion.
The magnetic field produced by the railways provides the possibility to explore theelectromagnetic fields that surrounds us. Measurements can be successfully compared with estimationsbased on reasonable data and information available on the internet. This experiment encourage student togo outdoors and experiment using everyday tools.
References [1] N. Silva, "Magnetic field sensor,"
Phys. Teach. (6), 372 (2012).[2] R. D. Septianto, D. Suhendra and F. Iskandar, "Utilisation of the magnetic sensor in a smartphone forfacile magnetostatics experiment: magnetic field due to electrical current in straight and loop wires," Phys. Educ. (1), 015015 (2017).[3] M. Monteiro, C. Stari, C. Cabeza, and A. C. Martí, "Magnetic field ‘flyby’ measurement using asmartphone’s magnetometer and accelerometer simultaneously," Phys. Teach. (9), 580 (2017).[4] V.O.M. Lara, D.F. Amaral, D. Faria, and L.P. Vieira, "Demonstrations of magnetic phenomena:measuring the air permeability using tablets," Phys. Educ. (6), 658 (2014).[5] E. Arribas, I. Escobar, C.P. Suarez, A. Najera, and A. Beléndez, "Measurement of the magnetic fieldof small magnets with a smartphone: a very economical laboratory practice for introductory physicscourses," Eur. J. Phys (6), 065002(2015). [6] S. Arabasi and H. Al-Taani, "Measuring the Earth's magnetic field dip angle using a smartphone-aidedsetup: a simple experiment for introductory physics laboratories," Eur. J. Phys. (2), 025201 (2017).[7] S. Staacks, S. Hütz, H. Heinke, and C. Stampfer, “Advanced tools for smartphone-based experiments:phyphox,” Phys. Educ. (4) 045009 (2018). [8] M. Monteiro, C. Stari, C. Cabeza, and A. C. Martí, “An Approach to Teach Error Analysis andUncertainties based on Mobile-device Sensors,” arXiv preprint arXiv:2005.13617 (2020). IGURES
Figure 1. The magnetic field measurement was taken by a pedestrian walking on an overpass above thetracks (left panel) shown in the satellite view (right panel). Axis x points in the direction of the currentsthrough the tracks (opposite to the current I , through the catenary) y is along the smartphone’s path, and z points vertically upwards. B = 24.6 μT is the horizontal component of Earth’s magnetic field (fromNOAA). Magnetic declination δ = 3.5º (from NOAA). Vertical component of Earth’s magnetic field is -39.6 μT (from NOAA). From map, angle θ = 59º. igure 2. Layout of the currents and the smartphone’s path. There is a current with intensity I through thecatenary and two returning currents of intensities I/2 on the tracks. The standard gauge railways andheight of the catenary were taken from the website of the company while the height of the bridge wasestimated from the pictures. igure 3.igure 3.