Readers, forgive me, for I have sinned. I have not taught my AP physics B class how to sketch electric field lines.
Now, before you call the official College Board Audit Police, I ask that you hear my reasons. After all, I certainly teach about electric fields in general, what electric fields do to a charge placed in them, and even how parallel plates or point charges can themselves produce electric fields. We even do an extensive variety of exercises in which we determine the magnitude and direction of the electric field produced by a multitude of charges at various positions in space. (See this post, for an example of fundamentals quiz questions on electrostatics.)
I’ve never introduced the field line representation formally. If I mention field lines at all, it’s because my class has done an old Physics Bowl test question asking about them. I’ll then note that field lines just tell us the direction of the electric field at any point, with the closeness of the field lines indicating the strength of the field. I say this in sort of “by the way” manner, making it clear that electric field lines are not something that the class needs to know about. And until this year, AP exams have not been particularly concerned about field lines and their meaning.[1]
Why don’t I pay more attention to field lines, which any physics professor would consider part of the cannon of introductory physics knowledge? Because first-year physics students have enough trouble merely understanding what an electric field is without trying to represent the electric field in an abstract way. On the rare occasions I have introduced field lines, students have tend to memorize pictures without grasping the reason for them. Second year students seem to get the idea, but newbies? Not a chance.
I may change my approach next year, if I can find a little bit of extra time. Martin Kirby, a fellow long time AP physics reader, described to me his approach to electric field lines. After his class has mastered[2] the idea of what an electric field is and what it means, he guides his students through a discussion of the electric field near a point charge. “Describe [in words] the electric field near this positive charge,” he says. His students indicate that the field points away from the charge, and is stronger near the charge than far away. Then comes the magic question:
“Okay, if you were asked to DRAW the electric field, how would you do it?” Then he lets the students chew on that for a while. They come up with all sorts of clever ideas, often involving the degree of shading, or colors, or annotations with numbers. After about 20 minutes of discussion and student attempts, he shows them an idea. “What if we drew lines,” he asks. “We point the lines in the direction of the field. The more lines we draw, and the closer those lines are to each other, the stronger the electric field.” Finally, Mr. Kirby shows the class how his idea works for a single point charge, as well as for two point charges.
Because the students have spent so much time trying to make their own representation of an electric field, they tend to latch on to Mr. Kirby’s simpler option.
[1] Take a look at 2009 AP physics B problem 2(a), which asks students to sketch electric field lines near two positive point charges.
[2] For the highest available value of “mastered,” of course
Now, before you call the official College Board Audit Police, I ask that you hear my reasons. After all, I certainly teach about electric fields in general, what electric fields do to a charge placed in them, and even how parallel plates or point charges can themselves produce electric fields. We even do an extensive variety of exercises in which we determine the magnitude and direction of the electric field produced by a multitude of charges at various positions in space. (See this post, for an example of fundamentals quiz questions on electrostatics.)
I’ve never introduced the field line representation formally. If I mention field lines at all, it’s because my class has done an old Physics Bowl test question asking about them. I’ll then note that field lines just tell us the direction of the electric field at any point, with the closeness of the field lines indicating the strength of the field. I say this in sort of “by the way” manner, making it clear that electric field lines are not something that the class needs to know about. And until this year, AP exams have not been particularly concerned about field lines and their meaning.[1]
Why don’t I pay more attention to field lines, which any physics professor would consider part of the cannon of introductory physics knowledge? Because first-year physics students have enough trouble merely understanding what an electric field is without trying to represent the electric field in an abstract way. On the rare occasions I have introduced field lines, students have tend to memorize pictures without grasping the reason for them. Second year students seem to get the idea, but newbies? Not a chance.
I may change my approach next year, if I can find a little bit of extra time. Martin Kirby, a fellow long time AP physics reader, described to me his approach to electric field lines. After his class has mastered[2] the idea of what an electric field is and what it means, he guides his students through a discussion of the electric field near a point charge. “Describe [in words] the electric field near this positive charge,” he says. His students indicate that the field points away from the charge, and is stronger near the charge than far away. Then comes the magic question:
“Okay, if you were asked to DRAW the electric field, how would you do it?” Then he lets the students chew on that for a while. They come up with all sorts of clever ideas, often involving the degree of shading, or colors, or annotations with numbers. After about 20 minutes of discussion and student attempts, he shows them an idea. “What if we drew lines,” he asks. “We point the lines in the direction of the field. The more lines we draw, and the closer those lines are to each other, the stronger the electric field.” Finally, Mr. Kirby shows the class how his idea works for a single point charge, as well as for two point charges.
Because the students have spent so much time trying to make their own representation of an electric field, they tend to latch on to Mr. Kirby’s simpler option.
[1] Take a look at 2009 AP physics B problem 2(a), which asks students to sketch electric field lines near two positive point charges.
[2] For the highest available value of “mastered,” of course
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