In the Classroom edited by
Applications and Analogies
Arthur M. Last University College of the Fraser Valley Abbotsford, BC, Canada
Known-to-Unknown Approach To Teach about Coulomb’s Law
P. K. Thamburaj Department of Chemistry, Ohio University Center, Zanesville, OH 4370;
[email protected] In introductory chemistry courses, students encounter various types of relationships among properties of matter. Published literature has demonstrated that analogies from life experiences help students comprehend those relationships taught in an introductory chemistry course (1–6). When a relationship links more than two variables and is somewhat complicated, such as Coulomb’s law, students struggle. Most popular text books have adequate discussion about the influence of charges and sizes of ions on a number of physical properties including lattice energy, melting point, and solubility of ionic substances (7, 8). A clear understanding of the relationships presented by Coulomb’s law is necessary for students to comprehend the effects of sizes and charges of ions on physical properties of ionic substances. An example from life experience that is parallel is presented here. As a mathematical equation, Coulomb’s law may be expressed as follows: q q F ∝ 1 22 (1) d or F =
k q1 q2
(2) d2 where F is the force (attraction or repulsion) between two charged particles, q1 and q2 are the magnitudes of charges on the particles, d is the distance between the charges, and k is the proportionality constant. Thus, according to this law, the force between two charged particles is directly proportional to the magnitudes of the charges and is inversely proportional to the square of the distance between them.1 It is the author’s experience that the majority of students in an introductory chemistry class are familiar with the process of covering floors with tiles. Most commercial floor tiles are sold as squares, with sides measuring 1, 1.5, or 2 in. To determine the number of tiles needed to cover a rectangular
Table 1. Dependency of Number of Tiles Needed (n) on Length (L) and Width (W) of a Room and the Size of the Square Tile (S)
room, one needs to know the length and width of the room and the size of the tile. The data in Table 1 illustrate how the number of tiles is dependent upon the length and width of the room and the size of the tile. A comparison of cases 1 and 2 in Table 1 demonstrates that the number of tiles needed is directly proportional to the length of the room while a comparison of cases 2 and 3 shows that the number of tiles is directly proportional to the width of the room. However, when we compare the data in cases 3, 4 and 5, we notice an inverse relationship between the number of tiles needed and the size of the tile. When the size of the tile is doubled, as in cases 3 and 4, the number of tiles is reduced by a factor of 4. An examination of cases 3 and 5 reveals that when the size of tile is halved, the number of tiles is increased by a factor of 4. These observations demonstrate that the number of tiles needed is inversely proportional to the square of the size of the tile used. The teacher may choose to illustrate the process using overhead transparencies and color coded mini square tiles. A comparison of cases 1 and 2 in Table 2 demonstrates that force is directly proportional to the magnitude of charge 1 (q1 ) while a comparison of cases 2 and 3 shows that the force is directly proportional to the magnitude of charge 2 (q2 ). However, when we compare the data on cases 3 and 4, we notice an inverse relationship between the force and distance between the charges. When the distance is doubled, as in cases 3 and 4, the force is reduced by a factor of 4. The force is inversely proportional to the square of the distance between the charged particles. Data on Table 2 relevant to Coulomb’s law show a definite parallel relationship to the ones associated with determining the number of tiles in Table 1. Students at this point are convinced that the relationships found in Coulomb’s law are no more complex than laying square tiles to cover the floor of a room. Students seem to relax when they realize that this type of complex relationship exists not just in science but in real life as well.
Table 2. The Dependence of the Force between Two Charged Particles (F) on the Magnitude of the Charges on the Particles (q1 and q2) and the Distance between Them (d)
Case
L/m
W/m
S/m
Number of Square Tiles
Case
q1/C
q2/C
d/m
Force/N
1
10.0
10.0
1.0
100
1
1.0
1.0
1.0
1.0
2
20.0
10.0
1.0
200
2
2.0
1.0
1.0
2.0
3
20.0
20.0
1.0
400
3
2.0
2.0
1.0
4.0
4
20.0
20.0
2.0
100
4
2.0
2.0
2.0
1.0
5
20.0
20.0
0.50
1600
Note: F = kq1q2/d2, where k = 1 (N m2)/C2 for the sake of simplicity.
NOTE: n = LW/S2
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Vol. 84 No. 3 March 2007
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In the Classroom
Note 1. The author is indebted to one of the reviewers for suggesting the sketch shown in Figure 1. The sketch illustrates that when the distance between two charged particles increases, the area experiencing the lines of force also increases. Point “A” on the sketch represents the position of a charged particle. When the distance is doubled (For example, when AC = 2 AB) the area experiencing the force is quadrupled (4 squares vs 1 square) and the intensity of the force is reduced to one fourth.
Acknowledgment The author appreciates the help of Pramod Kanwar at Ohio University Center in Zanesville, Ohio in drawing the sketch. Literature Cited 1. 2. 3. 4. 5.
Figure 1. Sketch illustrating that when the distance between two charged particles increases, the area experiencing the lines of force also increases.
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Fortman, John J. J. Chem. Educ. 1993, 70, 649. Fortman, John J. J. Chem. Educ. 1994, 71, 848. Umland, Jean B. J. Chem. Educ. 1984, 61, 1036. Thamburaj, P. K. J. Chem. Educ. 2001, 78, 915–916. Haim, L.; Corton, E.; Kocmur, S.; Galagovsky, L. J. Chem. Educ. 2003, 80, 1021–1022. 6. Cain, Linda. J. Chem. Educ. 1986, 63, 1048. 7. Kotz, J. C.; Treichel, P., Jr. Chemistry and Chemical Reactivity, 5th ed.; Thomson: Belmont, CA, 2003; pp 93, 329–331. 8. McMurry, J.; Fay, R. C. Chemistry, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 2001; pp 213–214.
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