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Solving Non-Intuitive Problems in E&M Adam Erickson, Research Advisor: Mano Singham Department of Physics, Case Western Reserve University ABSTRACT We analyzed the problem-solving strategies of individuals with varying experience in physics in a conceptually difficult question. An extremely simple direct current circuit with a qualitative question concerning its flow of energy was presented to novice, intermediate, and expert problem solvers. The results indicate that many students are inclined to think energy flows through the wires, and is carried by current. Intermediate problem solvers (upperclassmen Physics majors) were able to recognize their incorrect preconception and offer alternative solutions. This contrasted with introductory-level students who could not expand on other possible solutions when made aware their initial ideas were incorrect. Expert problem solvers consisted of physics professor. They proved to not only offer the most knowledge on the topic of energy in E&M, but also demonstrated superior problem solving skills. This investigation covers the key features of the responses of the three groups, which leads to a marked improvement as we move along the spectrum of novice to expert problem solvers. BACKGROUND Lillian McDermott conducted extensive research on misconceptions in E&M, however energy flow in DC circuits was never investigated. We have modeled an exploratory experiment after Chandralekha Singh’s research of a nonintuitive mechanics question that was answered by Physics professors and introductory students.. We posed a conceptually difficult question to three groups, novice, intermediate, and expert problem solvers. They were given minutes to provide an answer. Responses were given verbally to best follow the problem solving strategies. Areas of interest include how problem solving differs among novel and expert problem solvers, as well as quantifying level of understanding energy in E&M among individuals of various experience in physics. In order to find the orientation of the Poynting vector throughout this circuit, the E and B fields must be determine. The orientation of these fields can be seen in Figure 2. The B field is a consequence of Ampere’s Law. ACKNOWLEDGEMENTS I would like to give a special thanks to Mano Singham, Prof. Chottiner, Brown, and Singer. Also Prof. Buxton for generously sacrificing both class time and extra credit. Many thanks also to all the participants who volunteered their time to answer the question. Without their time this project would not have been possible. FUTURE WORK This was an exploratory project, so one question to consider is, what changes would be made if I were to conduct these interviews again. My protocol impacted the participants’ responses (especially novices). No changes would be necessary for experts’ interviews. With the novices however, once the point of interest was reached, the interview did not progress much further. Perhaps major editing of the question would be appropriate, making the question posed to novices less open ended. -Intermediates - Intuition led 6 of 7 participants to initially say the energy was carried by current/flowed in wires. All discovered the contradiction that results from this from this statement. In their attempts for alternate solutions, many approaches were taken. These include looking at the microscopic level, thinking of the circuit as two levels of potential energy, and the idea that fields are transporting energy. From 7 volunteers, 2 offered satisfactory answers. -Experts - The responses from every professor was lengthier than the novices. Perhaps this is a sign of internal questioning, a sign of more advanced problem solving skills. This was also the only group with participants that made the use of analogies. The experts showed both a better approach to problem solving as well as a greater understanding on the topic of energy in E&M. These two factors contributed to 4 of 6 participants giving satisfactory explanations on the path of the energy in the described circuit. SOLUTION To determine how the energy is being transferred in this circuit, the E and B fields must be considered. When these field are found, the cross product of them can be taken to find the Poynting vector. The Poynting vector is defined as the energy per unit time, per unit area transported by the E and B fields. It is quantified as follows: The cross product is illustrated in Figure 1. Figure 1: Resulting S vector from cross product of E and B. Since the wires have resistance, an E field points along them, driving the current. Because there is a potential drop along the wire, there is also an E field just outside the wire, parallel to the surface. With the orientation of these fields known, the Poynting vector can now be found throughout the circuit. Figure 2 : The circumscribed dots represent the B field pointing out of the paper, the circumscribed crosses represent the B field pointing into the paper. The Poynting vector results from the cross product of E and B and is illustrated in Figure 3. In the following figure, the Poynting vector is outward at the battery, and inward at the resistor (light bulb), indicating a flow of energy from the battery to the light bulb. The S vector is radially inward at the wires representing a flow of energy into the wire equal to the energy being lost in the wire in the form of heat. RESULTS The participants’ quality of responses showed a marked improvement as we moved up in each group. The key characteristic of each group are outlined below. Figure 3: The Poynting vector is illustrated here. Note it is outward at the battery and inward at the resistor (light bulb). -Novices - Responses were short and one thought long. All interviews reached a contradiction of constant current and theory of current carrying the energy. No alternate solutions were mentioned. Out of 8 total participants, none offered a satisfactory solution. IMPLICATIONS FOR FUTURE E&M EDUCATION Results have shown us that in general students at the introductory level of E&M have little understanding on the flow of energy in DC circuits. Is this a problem? Perhaps not as a very thorough model can be made for the behavior of DC circuits without directly address where the energy is. This would also be a difficult concept to handle when learning basics of E&M. Consider the simple circuit to the left containing a battery and a light bulb. When current is flowing, the bulb will light up, emitting energy in the form of heat and light. Explain qualitatively how the energy gets from the battery to the light bulb. THE QUESTION

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