Antara Sen, M.C. Sullivan
Multipole expansions of electric charge and current distributions and the fields those multipoles create are a fundamental pillar of electromagnetic theory, but explanations and examples are rare beyond a dipole. In this paper we describe a low-cost exploration of magnetic multipoles. Using the field from ideal magnetic dipoles and a simple binomial approximation, we show that each multipole obeys B∝rn, with n=−3,−4,−5,−6 for a dipole, quadrupole, sextupole, and octupole, respectively. Using commercially available NdFeB magnets and the magnetic field sensor inside a smartphone, we experimentally verify the power-law dependence of the multipole configurations. Finally, the open-source Python library Magpylib can simulate the magnetic field of arbitrary permanent magnet distributions, which also shows the same power law dependence for the different multipole configurations.
Comments: 7 pages, 9 figures
Modern Physics demonstrations with DIY Smartphone Spectrometers: https://arxiv.org/abs/2203.12015
Aarushi Khandelwal, Tze Kwang Leong, Yarong Yang, Loo Kang Wee, Félix J. García Clemente, T Venkatesan, Hariom Jani
Smartphones are widely available and used extensively by students worldwide. These phones often come equipped with high-quality cameras that can be combined with basic optical elements to build a cost-effective DIY spectrometer. Here, we discuss a series of demonstrations and pedagogical exercises, accompanied by our DIY diffractive spectrometer that uses a free web platform for instant spectral analysis. Specifically, these demonstrations can be used to encourage hands-on and inquiry-based learning of wave optics, broadband vs discrete light emission, quantization, Heisenberg's energy-time uncertainty relation, and the use of spectroscopy in day-to-day life. Hence, these simple tools can be readily deployed in high school classrooms to communicate the practices of science.
Comments: 7 pages, 7 figures