Demonstration Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
pubs.acs.org/jchemeduc
Measuring the Force between Magnets as an Analogy for Coulomb’s Law Samuel P. Hendrix† and Stephen G. Prilliman* Department of Chemistry, Oklahoma City University, Oklahoma City, Oklahoma 73106, United States S Supporting Information *
ABSTRACT: A brief demonstration is described that measures the force between magnets as an analogy for the force between charged particles to introduce the functional form of Coulomb’s law. One magnet is mounted on a digital force probe while another is systematically moved to different distances to measure the force as a function of distance. The force probe and magnets are held in place with plastic interlocking building bricks. The demonstration is used as an analogy to introduce students to the physics of electrostatic forces, a foundational principle for understanding chemical phenomena such as ionization energy, bonding, intermolecular forces, and lattice energy.
KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Demonstrations, Analogies/Transfer, Inquiry-Based/Discovery Learning
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INTRODUCTION The electrostatic force, the force exerted between charged particles, is used to interpret many chemical phenomena including periodic trends, covalent bonding, intermolecular forces, and lattice energy. The electrostatic force is governed by Coulomb’s law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between the charges: F=
The need for a deep conceptual understanding of Coulomb’s law can be seen in the research on students’ understanding of ionization energy. Both students7−10 and preservice teachers11,12 have been found to hold misconceptions about ionization energy. One common belief is that atoms and ions with filled/half-filled shells or a complete electron octet possess unusual stability. Another misconception is that nuclei have a certain amount of force (dependent on nuclear charge) which is distributed among electrons, a conception Taber calls “conservation of force”.7 This concept is non-Coulombic in nature since any two charged particles are attracted or repelled regardless of other charged particles interacting with the first two particles. Even if misconceptions are not present, students in introductory chemistry have not yet have covered Coulomb’s law in introductory physics. Here we present a brief demonstration for introducing Coulomb’s law using an analogous situation, the force between magnets. The demonstration shows the distance dependence and the sign of force for attraction and repulsion. The setup utilizes plastic interlocking building bricks to firmly hold the strong magnets needed to generate measurable forces while also allowing the distance between the magnets to be varied quickly and systematically. Magnets have been used repeatedly as models for electrostatic phenomena in chemistry including covalent bonding,13−16 bonding in solids,17 VSEPR theory,18−21 and water and solutions;22−24 as an analogy for the Millikan oil-
kq1q2 r2
where k is a constant, q1 and q2 are the value of the charges 1 and 2, and r is the distance between the charges. Particles of like charge produce a repulsive (algebraically positive) force, while particles of opposite charge produce an attractive (algebraically negative) force. The importance of Coulomb’s law at the introductory level can be seen in the Advanced Placement (AP) Chemistry Curriculum Framework where it is referenced throughout the first two of the curriculum’s six “Big Ideas”.1 Questions involving Coulomb’s law have appeared on the free response section of recent AP exams.2,3 The Next Generation Science Standards (NGSS) include two high school learning objectives on Coulomb’s law in a chemistry context (HS-PS1-1 and HSPS2-6).4,5 The National Research Council’s Framework for K-12 Education, the basis for the NGSS, summarizes the importance of these concepts: “The structure and interactions of matter at the bulk scale are determined by electrical forces within and between atoms.”6 © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: August 1, 2017 Revised: March 6, 2018
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DOI: 10.1021/acs.jchemed.7b00580 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Demonstration
drop experiment;25 and as a representation of nucleophilic and electrophilic centers in organic reaction mechanisms.26 Analogies have been shown to be effective in science teaching so long as the analogous system is sufficiently similar and is fully mapped onto the system of interest, and as long as breakdowns in the analogy are explored.27 The demonstration is executed using the predict−observe−explain model28 with students working in small groups to create the opportunity for students to discover, confront, and overcome their own misconceptions as well as map the analogy from the observed magnetic system to the target system of charged particles.
mounted with their centers aligned as nearly as possible with the sensor-mounted magnet. As shown in Figure 2, the force
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HAZARDS Neodymium (or rare-earth) magnets should be purchased, handled, and stored with care. Swallowing of rare-earth magnets can lead to death in children. The packaging of the magnets used here recommends they not be used with children under age 15.
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DEMONSTRATION The device consists of a digital force probe in a box of LEGO brand interlocking building bricks measuring 14 studs × 8 studs (112 mm × 88 mm) on a base formed by four 1/3-height 12 stud × 6 stud sheets (Figure 1, see Supporting Information for
Figure 2. Graph of the data collected in the repulsive arrangement with images of the magnet position shown below the corresponding data point. The distance between the magnets is varied by moving the bricks on which the opposing magnet is mounted back one stud (8 mm) at a time.
can be measured at different distances by detaching the doublestacked 2 × 6 stud bricks from the base and iteratively moving them one stud farther (8 mm) from the sensor magnet. Critically, the building bricks grip one another strongly enough that the opposing magnet will remain firmly in place once moved. The sensor is connected to a computer to project the data for students as it is collected. Before the opposing magnet is placed on the setup, the force value is zeroed in the software and values are set to “Reverse” so that the attractive force is registered as negative values in accord with convention. Measurements are recorded using Vernier LoggerLite software in the “events with entry” mode with the entry distance and the unit millimeters. The initial distance in our setup is 5 mm, and each iteration is 8 mm farther from the last. The demonstration is performed using the predict−observe− explain model.28 Before the demonstration, students are organized into groups of three or four and given the demonstration handout (see Supporting Information). The handout describes the procedure, and students are asked to discuss and draw their prediction of the results on a blank set of axes. After each group signals that they have written their prediction the demonstration is executed. A clear 1/r2 force− distance curve results with the force reaching nearly zero by about the fifth stud (37 mm separation) (Figure 3). The data collection takes only 1−2 min. After the demonstration, student groups are asked to record the observed data, compare these to their predictions, and discuss any discrepancies. Students are then asked to predict the results using attractive magnets, and the demonstration is repeated with magnets using the attractive opposing magnet. Following the second demonstration, students are given several questions to prompt them to map the analogy from the magnets to systems of charges (see Supporting Information).
Figure 1. Demonstration setup. A box is built using plastic interlocking building bricks to encase the sensor but allow the sensor bolt to be unimpeded. One neodymium magnet is glued to the sensor bolt while the other is glued to a movable interlocking brick. A thin piece of cork acts as a spacer between the two magnets.
detailed instructions). The small space between the sensor housing and the building brick compartment is filled with either heavy paper or mounting tape to minimize any movement of the sensor housing during the demonstration. The hook provided with the sensor is unscrewed and replaced with a 1 in. (25 mm), #6-24 thread bolt. The head of this bolt is glued to one 1/2 in. (12 mm) diameter neodymium magnet, 1/8th in. (3 mm) thickness, using super glue. An 1/8th inch (3 mm) thick piece of cork is cut to match the size of the magnet and glued onto its face as a spacer. The spacer makes it easier to separate the magnets in case they snap together during the demonstration. The opposing magnets are glued to two separate double-stacked 2 stud × 6 stud building bricks. One opposing magnet is oriented such that it will have a repulsive interaction with the sensor-mounted magnet and the other will have an attractive interaction. The opposing magnets are B
DOI: 10.1021/acs.jchemed.7b00580 J. Chem. Educ. XXXX, XXX, XXX−XXX
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deviations from the 1/r2 distance dependence.34−36 The use of magnets has several advantages. The demonstration is fast, robust, and reliable and can easily be quickly switched between attractive and repulsive configurations. Because force is directly observed no calculations are necessary to transform the data. Although it relies on an analogy, it is one with which students have some familiarity making it more likely to be useful.27 Analogies are important tools for teaching but should be accompanied by a discussion of the uses and limitations of the analogy.27 In this demonstration, it should be emphasized to students that magnets are not an exactly analogous to charges.23,37,38 It is important to point out that protons and electrons interact through electrostatic, not magnetic, forces. Students should also recognize that magnets always exist in dipoles (north and south), while positive and negative charge can and do exist as independent monopoles. To help achieve this understanding, the postdemonstration activity provides several discussion questions to help students map the analogy onto the target system.
Figure 3. Force versus magnet separation. Magnets are in the attractive orientation, and initial magnet separation is 5 mm. Inset is the force versus the inverse square of the distance with a linear trend line (R2 = 0.991).
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CONCLUSION A thorough conceptual understanding of Coulomb’s law is an essential first step for students to move beyond memorized answers or misconceptions of atomic and molecular properties. The demonstration presented here provides chemistry instructors a quick and robust way to introduce Coulomb’s law through an analogy with magnets. Executing the demonstration with the predict−observe−explain method helps ensure that students are engaged with the demonstration, helps reveal and confront misconceptions, and moves chemistry students toward a much needed conceptual understanding of electrostatic interactions.
If instructors desire more data points on the curve, an alternative procedure is provided in the Supporting Information which allows magnets to be placed at “half stud” (4 mm) increments.
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DISCUSSION Many students find that their predictions differ from the actual results. The most common student mistakes are (i) graphs of the wrong functional form (usually linear), (ii) graphs that increase instead of decrease with distance, and/or (iii) graphs that have the wrong sign for attractive and/or repulsive cases. Students may also be unfamiliar with the concept of asymptotes. Students will sometimes work around this by drawing a line with a negative slope that stops before it crosses the distance axis. Plastic interlocking building bricks have been used previously in lab settings described in this Journal to build UV and visible spectrometers.29−32 Interlocking building bricks were employed here because, once constructed, they are extremely stable and rigid. Having the opposing magnet glued to a brick allows it to be moved to new positions but remain stationary once in that position. This configuration also eliminates the need to measure the distance between magnets each time. Instead, instructors need only measure the initial distance and then add 8 mm for each time the magnet distance is increased as shown in Figure 2. Because the bricks are plastic, they are also nonmagnetic, eliminating additional forces present in setups created from steel parts. Building bricks are relatively low cost. Those used in this were purchased loosely for about $15. The force sensor is the largest cost in the demonstration. If an adequate sensor can be borrowed from a colleague teaching physics, the total cost of the demonstration is approximately $25. Demonstrations of Coulomb’s law found in the physics education literature using charged balls either suspended from a string,33 a weighted torsion balance,34 or one stationary ball repelling another ball mounted on an electronic balance.35,36 The charged balls demonstrations can be carried out quite cheaply, but the balls are subject to charge leakage and are subject to nonuniform charge distribution, resulting in
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00580. List of materials, step-by-step instructions for building the demonstration, and student handouts for predicting/ recording the observations of the demonstration and mapping the analogy from magnets to charges (PDF, DOCX)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Stephen G. Prilliman: 0000-0002-9699-3638 Present Address †
Putnum City North High School, Oklahoma City, OK 73162.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors wish to thank the reviewers for their suggestions. S.G.P. thanks Jude G. Prilliman for sharing his building blocks expertise. C
DOI: 10.1021/acs.jchemed.7b00580 J. Chem. Educ. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jchemed.7b00580 J. Chem. Educ. XXXX, XXX, XXX−XXX
