Analysis and comparison of students’ conceptual understanding of symmetry arguments in Gauss’s and Ampere’s laws

Campos, Esmeralda; Hernandez, Eder; Barniol, Pablo; Zavala, Genaro

doi:10.1103/physrevphyseducres.19.010103

Cited by 7 publications

(8 citation statements)

References 27 publications

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“…Experimental results agree with the expectations within less than two standard deviations, being 2.5 ± 0.3. The main results are summarised in table 4.…”

Section: Results With Smartphonesmentioning

confidence: 99%

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A modern, rapid and simple investigation of Ampère’s law

Cicuta,

Organtini

2024

Phys. Educ.

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Classical physics results are often taught purely from the theoretical side. Key results, especially in electromagnetism, are typically not explored experimentally, and in applications students are then expected to leap straight into more complex scenarios that make use of these principles in electronics, sensors and instrumentation. This is unfortunate because not all individuals are equally able to learn well purely from the mathematical angle, and even those who do are not exposed to exploring the magnitude of competing effects, for example isolating a particular magnetic field signal from the background of the Earth’s field. An experiment is presented here to test Ampère’s law with a setup that can be assembled out of everyday materials with minimal components—a smartphone, a DC power supply, wires—in a procedure that can be completed in just a few hours. The data from the three magnetic field sensors of the phones, together with the gyroscope sensors providing position, are recorded and numerically integrated. The experiment is also demonstrated using sensors collected by an Arduino board instead of a smartphone. The experiment allows to measure the net current carried by wires inside the closed path over which the magnetic field is integrated, i.e. Ampère’s law. This experimental approach to exploring Ampère’s Law can be adapted towards high school or university demonstrations, depending on the level of accuracy and detail that one aims to pursue.

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“…Experimental results agree with the expectations within less than two standard deviations, being 2.5 ± 0.3. The main results are summarised in table 4.…”

Section: Results With Smartphonesmentioning

confidence: 99%

“…After a comparative study [4] of the students' difficulties in understanding Ampère's and Gauss Laws, the authors suggest that including 'active learning activities where the students have the opportunity to reflect on the application of Gauss's and Ampère's laws' is important.…”

Section: Introductionmentioning

confidence: 99%

A modern, rapid and simple investigation of Ampère’s law

Cicuta,

Organtini

2024

Phys. Educ.

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“…Based on the literature about interference between electricity and magnetism concepts and our observations while analyzing the data for previous studies (Barniol & Zavala, 2015, Campos et al, 2023Hernandez et al, , 2021Hernandez et al, , 2022, we found the opportunity to identify how some elements of magnetism may be present when students reason about Gauss's law, and elements of electricity may be present when students reason about Ampere's law. By the elements of electricity or magnetism, we mean specific words in students' explanations or specific letters in students' written equations that hint at the opposite context (for example, calling the electric field the "magnetic field").…”

Section: Research Questionsmentioning

confidence: 99%

“…The questionnaires use parallel representations, a characteristic further exploited in the related publications (Campos et al, 2021(Campos et al, , 2023Hernandez, , 2022.…”

Section: / 12mentioning

confidence: 99%

Learning interference between electricity and magnetism? Analysis of patterns and consistency

Campos

Hernandez

Barniol

et al. 2023

EURASIA J Math Sci Tech Ed

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Due to the similarities between Gauss’s and Ampere’s laws, students can present cognitive interference when learning these laws in the introductory physics course. This study aims to analyze the interference patterns that emerge in students’ answers when solving problems that involve Gauss’s and Ampere’s laws and related concepts (e.g., electric flux and magnetic circulation). We conducted a study of 322 engineering students attending a private Mexican university. We applied two open-ended questionnaires with questions that prompted using Gauss’s and Ampere’s laws. We analyzed students’ answers to identify whether they presented some word or element of an equation from the opposite context and coded them into coding families. We analyzed the consistency of interference by counting the times each student presented some interference in general and by coding family. The results indicated that the interferences related to the shape of the Gaussian surface or Amperian trajectory and field-related concepts are shared among contexts. However, the interference related to the source of the field (charge or current) is predominant in magnetism. In contrast, the interference related to using elements from the opposite context in an equation predominates in electricity. In other words, students referred to currents as charges and wrote equations that contained B (for magnetic field) or other similar elements in Gauss’s law. The general consistency analysis revealed that around half the students presented at least one interference in both contexts. We recommend that the interference between electricity and magnetism in Gauss’s and Ampere’s laws must not be overlooked. This study’s findings can guide introductory and intermediate electricity and magnetism instructors to address this interference phenomenon.

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“…Additionally, Ampère's law is most effective when dealing with current configurations that exhibit symmetry, such as infinite straight lines, infinite planes, infinite solenoids, and toroids [5]. Demonstrations aimed at explaining and visualizing Ampère's law are available [6,7], yet students often struggle with the concepts of symmetry and the principle of superposition in grasping the magnetic field's conceptual framework [8,9].…”

Section: Introductionmentioning

confidence: 99%

Superposition principle with Ampère’s law and a semi-infinite wire

Kanchanapusakit,

Tanalikhit

2024

Phys. Scr.

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In this article, a semi-infinite wire serves as a pedagogical example to demonstrate Ampère's law. To effectively apply the law, two conditions must be met: (i) the wire must form a closed circuit, and (ii) the current must have symmetry. Fulfilling requirement (i) involves connecting an additional semi-infinite wire at an arbitrary angle, ensuring that their far ends join at infinity to form a closed circuit. Although this additional wire disrupts current symmetry, condition (ii) can be satisfied by superposing multiple diagrams wherein the additional wires are arranged with symmetry. Ampère's law can then be utilized to determine the magnetic field generated by the wire arrangement. The analysis in this article is well-suited for introductory electromagnetism courses, highlighting the principle of superposition in physics.

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Analysis and comparison of students’ conceptual understanding of symmetry arguments in Gauss’s and Ampere’s laws

Cited by 7 publications

References 27 publications

A modern, rapid and simple investigation of Ampère’s law

A modern, rapid and simple investigation of Ampère’s law

Learning interference between electricity and magnetism? Analysis of patterns and consistency

Superposition principle with Ampère’s law and a semi-infinite wire

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