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University Students’ Understanding ofElectromagnetic InductionJenaro Guisasola a , Jose M. Almudi b & Kristina Zuza ba Applied Physics, Escuela Universitaria Politécnica, Plaza Europa1, San Sebastian, 20018, Spainb Applied Physics, University of the Basque Country, SanSebastian, Guipuzcoa, SpainPublished online: 04 Oct 2011.

To cite this article: Jenaro Guisasola , Jose M. Almudi & Kristina Zuza (2011): University Students’Understanding of Electromagnetic Induction, International Journal of Science Education,DOI:10.1080/09500693.2011.624134

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University Students’ Understanding of

Electromagnetic Induction

Jenaro Guisasolaa∗, Jose M. Almudib and Kristina Zuzab

aApplied Physics, Escuela Universitaria Politecnica, Plaza Europa 1, San Sebastian

20018, Spain; bApplied Physics, University of the Basque Country, San Sebastian,

Guipuzcoa, Spain

This study examined engineering and physical science students’ understanding of the electromagnetic

induction (EMI) phenomena. It is assumed that significant knowledge of the EMI theory is a basic

prerequisite when students have to think about electromagnetic phenomena. To analyse students’

conceptions, we have taken into account the fact that individuals build mental representations to

help them understand how a physical system works. Individuals use these representations to explain

reality, depending on the context and the contents involved. Therefore, we have designed a

questionnaire with an emphasis on explanations and an interview, so as to analyse students’

reasoning. We found that most of the students failed to distinguish between macroscopic levels

described in terms of fields and microscopic levels described in terms of the actions of fields. It is

concluded that although the questionnaire and interviews involved a limited range of phenomena,

the identified explanations fall into three main categories that can provide information for

curriculum development by identifying the strengths and weaknesses of students’ conceptions.

Keywords: Electromagnetic induction; Students’ conceptions; University physics education

1. Introduction

Students’ difficulties in the field of physics have been analysed in numerous research

papers on physics education (Duit, 2007). Many of these alternative ideas have

been called ‘common sense’ because they are very widespread among students from

different countries and at different levels. These ideas are also linked to forms of

normal reasoning in everyday life, assumed by students prior to receiving any teaching

on the subject. The origin of any person’s current understanding is likely to include

International Journal of Science Education

2011, 1–26, iFirst Article

∗Corresponding author: Applied Physics, Escuela Universitaria Politecnica, Plaza Europa 1, San

Sebastian, 20018, Spain. Email: jenaro.guisasola@ehu.es

ISSN 0950-0693 (print)/ISSN 1464-5289 (online)/11/000001–26

# 2011 Taylor & Francis

http://dx.doi.org/10.1080/09500693.2011.624134

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both formal and everyday experiences. It is inappropriate to try to separate the aspects

of students’ understanding derived from the two forms of experiences (Driver, Leach,

Scott, & Wood-Robinson, 1994). While everyday experience makes an impact on

some alternative conceptions, some areas of physics have no obvious parallels in every-

day experience. Therefore, everyday prior experience plays a lesser role in terms of a

source for alternative conceptions. Electromagnetic induction (EMI) is one such

area. However, when students tackle problems on areas of physics far removed from

everyday experience, everyday forms of reasoning also emerge (Guisasola, Almudı,

Salinas, Zuza, & Ceberio, 2008; Viennot, 2001). Thus, with regard to these extremely

academic subjects, it is reasonable to think that it is particularly necessary to analyse

the meaning of physics contents to understand students’ answers. It is also necessary

to take into account the contemporary meaning of the concept included in EMI that it

will be discussed in the next section.

EMI is a fundamental topic within the undergraduate science and engineering cur-

riculum and the last year of secondary education (18 years old). EMI is a subject in

which different laws and concepts in the electrical and magnetic field are dealt with

together. Students have to apply their conceptions on basic concepts of electromag-

netism such as field, flux, and electromagnetic force. Moreover, previous studies

show students’ difficulties in analysing concepts such as magnetic flow or Faraday’s

law. Chabay and Sherwood (2006, p. 333) pointed out that ‘Faraday’s law is

usually difficult for students. Moreover, the integral form involves the concept of

flux, which is traditionally introduced at the start of the course in the context of

Gauss’ law and not mentioned again until the introduction of Faraday’s law’. The

topic is not only interesting for scientists or engineers, but it is also relevant for citi-

zens. Correctly interpreting EMI phenomena allows people to make informed

decisions regarding many applications of EMI in everyday life (induction cookers, elec-

tric motors, cellular phones, etc.). Nevertheless, the academic and social importance of

the topic, teaching–learning the explanatory theory of EMI phenomena, is a poorly

researched pedagogical problem, when compared with other physics subjects.

In introductory physics courses for science and engineering degrees, students learn

that EMI phenomena are due to a time-varying magnetic field or/and to the move-

ment of a conductor or circuit within a magnetic field. In particular, Faraday’s law

is taught to calculate the electromotive force (emf) induced. Students apply this law

to analyse simple cases, for example, to calculate the emf induced in a circuit,

which is in a time-variable magnetic field. However, Chabay and Sherwood (2006,

p. 333) pointed out that ‘Faraday’s law is usually difficult for students. Moreover,

the integral form involves the concept of flux, which is traditionally introduced at

the start of the course in the context of Gauss’ law and not mentioned again until

the introduction of Faraday’s law’. Similarly, Bagno and Eylon (1997, p. 330)

showed that ‘In students’ knowledge of representation there is an overemphasis on

subsidiary information at the expense of more central relationships. For instance,

many students consider Ohm’s law to be of central importance and completely disre-

gard electromagnetic induction’. This research, among other works, seems to indicate

that there is a problem in teaching EMI and, in particular, Faraday’s law.

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This paper will focus on the description of undergraduate students’ understanding

as data on which teachers can base their decisions about intervention to assist student

learning. The data also indicate ways of improving teaching sequence designs so as to

measure development of understanding. This paper describes some outcomes from

research into the assessment of students’ levels of understanding some key concepts

and principles in EMI. Levels of understanding are described here for two particular

phenomena involving EMI associated with a time-variable magnetic field and/or with

the movement of a circuit or part thereof in a time-constant magnetic field. We

focused on simple situations of circuits at rest or in motion, because these situations

are not mathematically complex which might mask conceptual difficulties. This

research into students’ knowledge of ideas and how to describe them can be used

when designing new teaching sequences.

This paper will first describe previous works that inspired the questions in this

research. Second, it will explain the theoretical framework for designing the research

instruments. Finally, it will show the results obtained and evidence for the defined cat-

egories. Learning more about students’ conceptions and their characteristics will be

useful to support new teaching programmes based on the active methodologies pro-

posed by current standards in science teaching.

2. Studies on Students’ Difficulties when Learning EMI and on the

Meaning of Faraday’s Law

EMI theory and Faraday’s EMI law, despite their widespread teaching in introductory

physics courses, continue to present challenges in terms of their interpretation

(Munley, 2004). Physicists recognise difficulties in understanding Faraday’s law of

EMI in certain situations. In 1964, Pugh stated that:

While the concepts concerning electromagnetism as covered by Maxwell’s equations

have been well established for some time, concerning certain phenomena, there still

exists some confusion in the minds of many who should have mastered the subject.

This fact has been impressed upon me by discussion with colleagues and with graduate

and undergraduate students. For example, analysis of emf produced by homopolar gen-

erator, Faraday disk, and similar devices still cause considerable difficulty. (Pugh, 1964,

p. 879)

Pugh concluded his study by recommending that EMI teaching should use a single

reference system based on combining Maxwell’s laws in differential form and Lor-

entz’s law (p. 883).

However, Tilley (1968) stated that:

The rule (Faraday’s flux rule) breaks down in situations where the material of the circuit

changes the ‘circuit’ is taken to be placed in a space where the current is. (p. 458)

Tilley presented an example where there is a great flux variation through the circuit,

but there is no induced emf. He stated that this example shows that Faraday’s ‘flow

rule’ has exceptions as already shown in the examples proposed by Feynman

(1964, p. 17–2).

University Students’ Understanding of Electromagnetic Induction 3

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The discussion on whether Faraday’s law is valid for all cases of EMI or whether it is

just a ‘rule’ with exceptions continued among the experts during the 1970s and 1980s.

Nussbaum (1972) stated that:

Some unusual circuits have been devised which appear to produce a flux change without

generating a corresponding induced potential difference, thus violating Faraday’s law.

What has been generated is a large amount of controversy (Pugh, 1968, Tilley, 1968,

Laithware, 1968, Beweley, 1952) and it is the purpose of this article to show the cause

of the dispute and its resolution. (p. 231)

Nussbaum (1972) demonstrated the validity of Faraday’s law for any situation as

long as:

the time rate of change of flux equals the introduced potential difference only when work

is performed in producing change. (p. 231)

Over the last decade of the twentieth century and the first decade of the twenty-first

century, discussions continued on the validity of Faraday’s law centred on cases of

EMI when the circuit is not properly defined for a finite interval of time. These

cases were the focus of previous discussions on exceptions to Faraday’s law. They par-

ticularly discussed the induction phenomena referring to conducting bodies or points

of contact in movement (Galili & Kaplan, 1997; Layton & Simon, 1998). Studies over

the last 10 years converge on indicating that there are no exceptions to Faraday’s law

of EMI if it is interpreted that Faraday’s law considered the surface area of the flow

integration such as that formed by moving the circuit or the conductor in movement

(Galili, Kaplan, & Lehavy, 2006; Munley, 2004). Munley (2004) showed in his study

that:

Faraday’s law, properly applied, can be used to calculate the induced emf in any situation

where the Lorentz force can be used. It is necessary that the circuit is instantaneously

fixed at all times in the conducting material and that the circuit changes continuously.

(p. 1483)

Galili et al. (2006) showed in their study that:

The treatment of open and composite circuits using eq. 1 = − dF

dtmight challenge

students who look for an area change. To find the latter they should create an imaginary

area that reflects the movement. The valid choice is provided only by Am as defined by eq.dAm

dt=

∮L

v�|dL. This area may have nothing to do with the area of the circuit in which the

electrical current is produced. (p. 340)

Having reached this point, we would like to direct the attention of the readers to the

textbooks written by Corson and Lorrain (1962); Lorrain, Corson, and Lorrain

(2000); and Cheng (1993) that show the conclusions presented below using detailed

mathematical calculations.

One last aspect that has been covered recently is the ‘causality’ of EMI. Jefimenko

(2004) demonstrated mathematically that the variables in Maxwell’s equations defin-

ing EMI are simultaneous over time and explained that they do not meet the principle

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of causality (all present phenomena are exclusively determined by past events). When

there is a variable electric field over time, there is simultaneously a variable magnetic

field over time. Jefimenko showed that:

According to these equations (Maxwell’s equations) in time-variable systems electric and

magnetic fields are always created simultaneously, because they have a common source:

the changing electric current ∂�J∂t

( ). Once created, the two fields coexist from then on

without any effect upon each other. Hence electromagnetic induction as a phenomenon

in which one of the field creates the other is an illusion. The ‘illusion of mutual creation’

arises from the facts that in time-dependent systems the two fields always appear promi-

nently together, while their causative sources (the time-variable current in particular)

remain in the background. (p. 295)

Hill (2010) insisted on the same issue of simultaneity of electric and magnetic fields

that are variable over time. Hill recommended that:

Introductory texts should offer this revised insight into Faraday’s law: This equation says

simply that a changing magnetic field is accompanied by a circulating electric field (both

are generated by a time-varying current density). (p. 411)

In this work, we have incorporated contributions from the aforementioned research

into designing the questions and their correction. However, we have considered stu-

dents’ answers to be correct if they spoke equivocally in terms of causality of the EMI,

because as Hill (2010) indicated, this is an aspect that is not contemplated by most

textbooks.

There are also studies on students’ understanding of EMI theory. Internationally,

there have been a modest number of studies into the problems associated with learning

on induced emf and Faraday’s law. Of those carried out, some have looked into the

general problems interpreting EMI phenomena. Loftus (1996) researched secondary

school students’ difficulties (14–18 years old) when interpreting three EMI phenom-

ena. In the first experiment, a ring was levitated over an electromagnet and then the

experiment was repeated with a ring that was open. When the ring was open,

despite the fact that the magnetic induction phenomenon occurred, there was no

current induced and so there was no force of repulsion between the electromagnet

and the ring. In the second experiment, it was observed that by passing a circuit

with a lamp and a solenoid over an electromagnet, the light came on. In the third exper-

iment, students had to explain a ferromagnetic cooking pot heating up on an induction

cooker. The study showed that only a few students were capable of interpreting each

experiment correctly. The author grouped together the incorrect answers into two

main patterns of reasoning common to several questions. One of the reasoning patterns

consisted of explaining that ‘something’ acts on another object ‘sending something’

(force, charge, light, etc.) along a specific path. The other reasoning pattern used

the fluid model in terms of explanations: something (force, charge, friction) ‘flows’

from one object to another. The study also showed that students had a problem

with action at a distance; some students believed that the electromagnet and the

ring, spiral, or pot must be physically joined for the effect to be transferred.

University Students’ Understanding of Electromagnetic Induction 5

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Other studies focused more on students’ understanding of Faraday’s law and the

concepts involved such as magnetic flow or change of magnetic flow. Mauk and

Hingley (2005) recounted the experience of preparing tutorials for 43 of their students

in the USA Air Force Academy (Colorado). They found that fewer than half the stu-

dents receiving traditional teaching can explain Faraday’s law correctly. Albe, Ventur-

ini, and Lascours (2001) produced a study on the difficulties encountered by first-year

physics students and students in teacher-training programmes, focused on the con-

cepts of magnetic field and magnetic flux. In conclusion, they indicated that in

both the groups, the majority of students could not give a correct meaning for the defi-

nition of flux and they confused it with magnetic field and with magnetic flux vari-

ation. In a later work, Venturini and Albe (2002) worked with first-year physics

students on their understanding of electromagnetism to investigate the difficulties

they encounter in understanding Faraday’s law. The results obtained showed that

19% of the students knew the correct mathematical definition, 27% gave answers

that were approximate, and only 10% made a correct interpretation of the law’s

equation. One of the research questions asked whether current has to be created by

induction in a closed circuit. The results indicated that 51% did not quote any

element, 22% described an experiment, and only 8% talked about flow variation.

At the University of Kuopio (Finland), Saarelainen, Laaksonen, and Hirvonen

(2007) carried out a study based on the well-known CSEM test (Maloney, O’Kuma,

Hieggelge, & Van Heuvelen, 2001). They gave this test to 144 first-year physics

students just as they began their course on electromagnetism with the aim of obtaining

a general snapshot of the students’ basic knowledge of the matter. They also inter-

viewed five of these students to study the conceptions and explanatory models used

by the students. In terms of the questions on EMI and Faraday’s law, they concluded

their work by commenting that the majority of the students did not understand the

concept of variation in magnetic flux as a basis for Faraday’s law. In addition, the

vast majority of the students did not even recognise the source of the magnetic field

or the conditions required to generate induced emf in simple examples of EMI.

Meng Thong and Gunstone (2008) interviewed 15 second-year physical science

students. The students had taken one course in electromagnetism in the first year

at university, and while the research was being carried out, they were doing laboratory

practicals, particularly working on qualitative explanations for electromagnetism

phenomena. In the part of the study on EMI, three alternative conceptions were

identified in the students: (1) the induced current varies proportionally to the

current that generates the induction; (2) there must be contact between the magnetic

flux and the external spiral if there has to be an induced emf (the field lines are under-

stood as real lines that make contact with the spiral); and (3) the difference in electro-

static potential is equal to the induced emf.

In summary, we can say that the few studies carried out with students in the last

years of secondary school and the first years of university identified some misunder-

standings and alternative conceptions from students, which can be summarised as

follows:

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(a) Many students understand magnetic flux as ‘flowing’ from the field or they

confuse it with the field itself (Albe et al., 2001; Venturini & Albe, 2002).

(b) Many students are not capable of giving examples of EMI and use Faraday’s law

without physical meaning (Mauk & Hingley, 2005; Meng Thong & Gunstone,

2008; Venturini & Alber, 2002).

(c) The vast majority of secondary school students and a significant part of first-year

university students do not recognise EMI phenomena traditionally taught in the

curriculum. A significant number use explanations based on transmitting a ‘force’

or ‘contact with the field’ (Loftus, 1996; Meng Thong & Gunstone, 2008).

(d) Many students interpret that the magnetic field produces the EMI (Mauk &

Hingley, 2005; Meng Thong & Gunstone, 2008).

In accordance with the literature review and the relevance of the EMI and its sources

in physics, in this study, we raise the following research questions:

. Which university students’ conceptions appear when explaining EMI phenomena?

. Can these conceptions be grouped in explanatory categories?

Regarding the first question, it is plausible that most university students show some of

the tendencies that we describe from the literature review. Most students find the

meaning of magnetic flux difficult or the fact that it varies as a source of EMI or

the meaning of Faraday’ law. This study will focus on describing students’ under-

standing as data on which teachers can base their decisions about intervention to

assist student learning.

3. Methodological Approach

Various techniques have been used to probe students’ conceptions. Different research

techniques have been shown to produce different results (Duit, Treagust, & Mansfield,

1996). Because students’ conceptions have been probed using different tasks in various

contexts, the consistency of these conceptions is an issue that must be taken into

account in research into students’ conceptions (Engel Clough & Driver, 1986;

Marton, 1981). This issue creates a need for research to describe the variation in stu-

dents’ conceptions. Phenomenography has been proposed and used to describe and

explain the variation in students’ conceptions (Marton, 1981; Marton & Booth, 1997).

This study uses the phenomenographic research approach to investigate ‘the quali-

tatively different ways in which people experience, conceptualise, perceive, and

understand various aspects of, and phenomena in, the world around them’

(Marton, 1981). As Marton and Booth (1997) said, ‘in phenomenography individuals

are seen as the bearers of different ways of experiencing a phenomenon and as bearers

of fragments of differing ways of experiencing that phenomenon’ (p. 114). The stu-

dents’ description attained is a collective description and, in that respect, individual

voices are abandoned.

Phenomenography deals with how different ways of perceiving and understanding

the reality (concepts and associated ways of reasoning) can be considered as categories

University Students’ Understanding of Electromagnetic Induction 7

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describing the reality. These categories can be observed among a great number of

individuals, and therefore all these representations together indicate a type of collec-

tive intellect. ‘The same description categories appear in different situations. The set

of categories is thus stable and can be applied, even if individuals “move” from one

category to another on different occasions’ (Marton, 1981, p. 195).

According to Marton and Booth (1997), creation of categories must follow a

specific set of criteria such as the following: (a) each category should be clearly

related to research phenomena, so that each one tells us something distinct about a

particular way of experiencing the phenomena; (b) Categories must be hierarchical

or, in other words, they must progress from simple to complex relations; and (c)

The categorisation system should be parsimonious, meaning that as few categories

as is reasonably possible should be explained. If the system of categories developed

meets the above criteria, it will be theoretically and pedagogically useful.

In this study, conceptions are presented in description categories following the cri-

teria proposed by Marton and Booth. These categories are drawn from questionnaire

and interview data; there is no attempt made to ‘fit’ the data into a predetermined cat-

egory. The categories are based on the most distinctive features that differentiate one

conception from another and are presented in the form of a hierarchy, reflecting

increasing levels of understanding. The hierarchy of the description categories

demonstrates the relationship between conceptions and provides a basis for decisions

about teaching and assessment.

4. Context of the Research and Methodology

The aim is to find out whether undergraduate students have understood the basic

ideas involved in EMI or, in other words, whether students understand: (a) that a

time-varying magnetic field induces emf; (b) the concept of motional emf; and (c)

EMI in terms of field (Faraday’ law) and in terms of the action of the field (Lorentz’s

force). All these concepts and theories are included as principal goals in the inter-

national standard teaching curriculum for introductory physics courses and in our

students’ curriculum, as we will explain below. We gave 102 students at the University

of the Basque Country (Spain) a questionnaire after they had studied the subject in

class. For a better understanding of how students think regarding EMI phenomena

and how they use Faraday’s law, 12 students were interviewed about their answers

to the questionnaire. The research described was carried out at the University of

the Basque Country over three years. All first-year students (36) had taken two

years of physics at high school and were doing their first physics course for engineers.

For the third-year physics degree, 36 students had completed the credits for the first

two years, specifically studying electromagnetism in the second year.

First-year engineering students received 3.5 h of lectures and spent 2 h in the lab-

oratory per week for 14 weeks (second semester) on electromagnetism. The lectures

were given by experienced teachers from the Department of Physics. EMI and

Faraday’s law were taught for two or three weeks of this course. The lectures and

problem-solving taught EMI phenomena, magnetic flux, induced emf and Faraday’s

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law, Lenz’s law, emf of movement, inductance, and RL circuits. Teaching also ana-

lysed in detail how to use Faraday’s law to calculate the emf induced by variation in

magnetic flux in situations where there is a time-variable magnetic field or when

there is a variation in the area involved in the integral of the flux due to the movement

of a circuit or part thereof. Around two lectures were devoted to explaining Faraday’s

law, and examples similar to those appearing in textbooks were given (Knight, Jones,

& Field, 2008). Situations where it is useful to take magnetic flux into consideration

were shown and analysed.

At the time of the research period, third-year physics students had taken a physics

programme in the first year, which had included the specifications described in the

preceding paragraph. A sample of third-year physics students was used with the inten-

tion of determining whether the difficulties found in first-year students persist during

instruction and constitute real teaching–learning problems.

Once the questionnaire had been prepared, we carried out a draft test with first-year

course students, which confirmed that students had no problem understanding how

the questions were formulated. Moreover, the aims of every problem situation pre-

sented were validated by six teachers (three from first-year engineering and three

from third-year physics). Students’ answers were analysed independently by the

researchers; Cohen’s kappa reliability coefficient averaged 0.84 for the questions,

indicating very good concordance in the judges’ criteria for setting the categories

described. The intra-rater reliability kappa coefficient was also calculated for the

main researcher three weeks later, obtaining a value of 0.88, on average, for all the

questions, which is satisfactory for a level of confidence of 95%. Finally, the questions

were included in the first-year students’ final examination and in the form of a pre-test

for third-year students who had already completed two semesters of electromagnetism

in the second year. The answers from the final questionnaire were analysed by the

three authors of this paper using the methodology described in Section 3. One of

the authors performed a preliminary analysis in which the answers were grouped

according to the explanations given by the students. The groups that emerged were

then discussed in a meeting in which each author analysed a sample representing

10% of the questionnaires. The original categories were redefined until a consensus

was reached. Each researcher then analysed each questionnaire individually (kappa

coefficient 0.82). Finally, a meeting was held in which all the answers were classified

and a consensus was reached on the answers where there had been some disagreement

(7% of the total).

The students’ answers to the questions were subjected to rigorous phenomeno-

graphic analysis. This involved one member of the research team reading the students’

answers and deriving a draft set of description categories for each question. The same

researcher then reread the students’ answers and tentatively allocated each answer to

one of the draft categories. The other researchers carried out the latter task indepen-

dently. Once the answers had been classified, answer allocations were compared. Any

disagreements about category description or answer allocations were resolved by

referring to the answers as the only evidence of students’ understanding. The focus

was on the students’ understanding, taking the students’ answer as a whole, rather

University Students’ Understanding of Electromagnetic Induction 9

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than on the occurrence of particular statements corresponding to a specific category

description. An iterative process was used to produce the final-category descriptions

that reflected similar understanding among answers allocated to each category and the

differences between the categories.

Semi-structured interviews were planned using POE (Prediction–Observation–

Explanation) tasks for a small sample of students from the two levels (White &

Gunstone, 1992, p. 44). The questions Q1, Q4, and Q7 from the questionnaire

were developed in the laboratory and the students were interviewed using these ques-

tion-like experiments. All the interviews were transcribed and the transcripts were sub-

jected to the same analysis described above. Interviewers attempted to encourage the

students to give full explanations of their understanding by non-directive questions

such as ‘What do you mean by that?’; ‘Could you explain that further?’; and ‘Do

you want to say anything else about this question?’.

The questions were given in three first-year engineering courses (N ¼ 102). As the

results did not differ significantly, they have been grouped together. The questions

were also given to all third-year physics students (N ¼ 36). Six students from the

first-year course and 12 from third-year physics were interviewed using the questions

Q1, Q4, and Q7.

5. Experimental Design

In this section, we describe the seven questions (see Appendix) completed by the stu-

dents and summarise the results. We briefly look at some answers which appeared on a

regular basis.

The first three questions dealt with EMI situations associated with a time-variable

magnetic field. These questions required students to recognise that a variation in a

magnetic field brings about a variation in magnetic flux through the chosen surface

and also to know that the time-varying magnetic field induces a non-conservative elec-

tric field that is responsible for the induced current if there is a circuit. The other four

questions involved EMI phenomena caused by the movement of a circuit or part

thereof in a time-constant magnetic field. The questions are familiar to students in

the academic context and are usually mentioned in textbooks as examples of EMI

phenomena.

5.1 A Time-Varying Magnetic Field Induces emf

The question Q1 deals with a circuit that is connected and located beside another

without a battery. This problem is similar to the textbook example of induced

current in a circuit (see, e.g. ‘Physics’ by Fishbane, Gasiorowicz, & Thornton,

1996, p. 839). The students had to explain why ammeter G registers a current. A

correct example from one of the students is given below:

When we have a circuit through which current I circulates, we know that a magnetic field

will be produced. As the circuit goes from having no current to having current I, this

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magnetic field B will be variable. This variable magnetic field (B) will produce an emf and

an induced current in the lower circuit. An induced current appears in the lower circuit

while there is a variable magnetic field, i.e. while there is a variation in intensity I in the

upper circuit.

This was the answer given by half of the first-year students and 70% of the third-year

physics students. In the next section, we will analyse the types of alternative answers

and their corresponding percentages.

For the question Q2, there is no magnetic induction because there is no time-

varying magnetic field and there is also no magnetic flux change.

The question Q3 is asked as an example of an induced current in a circuit within a

variable magnetic field in many textbooks for introductory physics courses (Knight

et al., 2008; Tipler & Mosca, 2004). For this question, students were told that the

loop had an induced electric current and were asked to explain the origin of this

current. In order to reply correctly, students had to know that a non-conservative elec-

trical field is produced by a time-varying magnetic field and that this is responsible for

the electrical force which acts on the electrons producing the induced emf and the

movement of charges in the loop. In contrast to the previous question, very few

first-year students answered this question correctly. This discrepancy will be analysed

in the next section.

5.2 Motional emf

The questions regarding motional emf present phenomena involving emf induced in a

conductor through a magnetic field (motional emf). For the question Q4, students

had to know that when a conductor moves within a magnetic field, this exerts a mag-

netic force on the conductor’s charges. This magnetic force will bring about an

induced emf and an electric current in the loop. The correct answer may be explained

by using Lorentz’s law, which the students had repeatedly practised in the preceding

section on magnetic fields. However, most students avoided the question and

answered that there was an induced electric current due to there being a variation

in flux and they used Faraday’s law to calculate the emf of induced movement.

For the questions Q5–Q7, in order to explain the induced electric current correctly,

students could use Lorentz’s law (microscopic point of view). This would be the most

usual way according to standard textbook explanations. However, students could also

explain the question by using Faraday’s law and the fact that the emf induced is due to

the variation in the magnetic flux when the area changes (macroscopic point of view).

Therefore, students can justify the existence of an induced current in the copper

disc in terms of the forces acting on the electrons (Lorentz’s law) at a microscopic

level or in terms of the field and the variation in flux (Faraday’s law). For example,

in the question Q7, which involves Faraday’s unipolar generator, students were

asked to state whether there was an induced electric current and to justify their

answers. The students could use Lorentz’s law, which explains the movement of

charges in the copper disc due to the magnetic force exerted on the electrons by the

uniform magnetic force. The students could also explain the question by using

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Faraday’s law and the fact that the emf induced is associated with the variation in the

magnetic flux when the area changes. Quite a few papers have reported the expla-

nation of ‘Faraday’s unipolar generator’ by using Faraday’s law and that the current

produced may be explained both by Faraday’s law and by Lorentz’s law (Corson,

1956; Corson & Lorrain, 1962; Munley, 2004; Nussbaum, 1972). Further math-

ematical treatment of these ideas can be found in the work of Cheng (1993), who

showed that the emf induced in the circuit is due to the area swept by an element

of the circuit.

This double description in terms of field or of the actions exerted by the field on

matter appears frequently in physics and the students had studied it both in mechanics

(gravitational field) and in electricity and magnetism. Unfortunately, as we will see in

the next section, most students applied Faraday’s law incorrectly, reaching wrong con-

clusions, and, furthermore, did not use Lorentz’s law to explain the induced current,

which is how it usually features in the textbooks.

6. Results and Categories of Description

In this section, we give the results obtained for both groups of students for the seven

questions. In the discussions, we will identify some conceptual difficulties which seem

to be common in many students. This description of the students’ ideas will concen-

trate on some persistent specific difficulties and how we might interpret them.

The results of the students’ answers (N ¼ 102 in first year of engineering and N ¼ 36

in third year of physics) to the seven questions are given as percentages in Tables 1 and 2.

The detailed description categories are provided below. In the ‘variation of flux’ cat-

egory, the focus is on the magnetic flux variation as the cause of EMI. In this category,

Table 1. Results for the questions Q1–Q3

Description

categories

Percentages of answers in category type

Question Q1 Question Q2 Question Q3

First-year

engineering

Third-

year

physics

First-year

engineering

Third-

year

physics

First-year

engineering

Third-

year

physics

Variation in

magnetic fluxa49 70 58 78 68 33

Electromagnetic

force actingb– – – – 4 27

Presence of

magnetic field

38 17 22 16 22 35

Non-classifiable 9 13 10 5 – –

No answer 4 0 10 1 6 5

aCorrect answer at macroscopic level.bCorrect answer at microscopic level.

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Table 2. Results for the questions Q4–Q7.

Description categories

Percentages of answers in category type

Question Q4 Question Q5 Question Q6 Question Q7

First-year

engineering

Third-year

physics

First-year

engineering

Third-year

physics

First-year

engineering

Third-year

physics

First-year

engineering

Third-year

physics

Variation in magnetic

fluxa66 64 25 7 4 0 7 0

Electromagnetic force

actingb4 13 21 31 4 11 20 20

Presence of magnetic

field

– – – – 9 0 11 7

Incorrect analysis of

flux change

– – 25 33 47 57 41 47

Non-classifiable 18 20 16 22 20 18 17 15

No answer 12 3 13 7 17 14 4 11

aCorrect answer at macroscopic level.bCorrect answer at microscopic level.

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a distinction is made between the flux of field and the change of flux. The change of

flux can be obtained by changing the magnetic field over time and/or by changing the

area swept by a conductor or an element of the circuit. It uses Faraday’s law and con-

cepts at a macroscopic level. Some examples of this type of answer are given below:

When the lower spiral moves, the magnetic flux through it starts to vary, so according to

Lenz’ Law a current is induced that opposes this variation. (First-year engineering, Q4)

By changing the orientation of the spiral we change the angle between the field direction

and the normal direction perpendicular to the spiral area. The spiral orientation varies

and therefore the flux varies over time, inducing an emf and a current in the spiral.

(Third-year physics, Q4)

The area enclosing the rectangle created by the ‘vdt’ length is not constant and so

although the field is constant, the surface and the flux on this surface area are not,

thereby making the phenomenon of electromagnetic induction appear. (First-year engin-

eering, Q5)

The ‘electromagnetic force acting’ category considers induction associated with mag-

netic force acting on the conductor in movement or associated with the electrical force

produced by the non-conservative electrical field induced. There is a focus on force

concept and Lorentz’s law at a microscopic level. It is considered necessary to point

out the magnetic force or the electric force due to induced non-Coulombian electric

field to explain the movement of charges and EMI. Some examples of this type of

answer are given below:

By moving the spiral in a magnetic field, a force occurs on the charge bearers (electrons)

according to Lorentz’ force. (Third-year physics, Q3)

There will be induction because a magnetic force will act on the electrons in the copper

wire that is moving in a magnetic field. (First-year engineering, Q6)

The copper wire moves in a magnetic field and the moving charges in the wire undergo

the force of the magnetic field. Induction will occur in a very short interval of time as

the magnetic force equals the gravitational force Fe¼ Fm there will be no current.

(Third-year physics, Q6)

There will be electromagnetic induction as we have a copper disk moving in a magnetic

field. The magnetic field exerts a force on the electrons and there is an induced current

that will tend to slow the disk down. (First-year engineering, Q7)

The ‘presence of magnetic field’ category focuses on the magnetic field, whether vari-

able or not, which produced the EMI. When there is an electric current, it produces a

magnetic field and so this magnetic field produces EMI. Some examples of this type of

answer are given below:

Crossing the solenoid, the magnetic field will produce the magnetic induction phenom-

enon that will generate an induced current in the opposite direction to the field that

generates it. (First-year engineering, Q2)

Yes, magnetic induction occurs as the solenoid crossing the field creates a flux that

produces magnetic induction. (Third-year physics, Q2)

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By bringing the magnet closer to the spiral, a magnetic field is created in the spiral. This

magnetic field exerts forces on the charges and produces the induction. (First-year engin-

eering, Q3)

There is induction because the disk is inside a magnetic field. (Third-year physics, Q7)

In the ‘incorrect analysis of flux change’ category the focus is on Faraday’s law, but in

contrast to the ‘variation of flux’ category, it confuses the surface of the conductor or

circuit with the surface swept by the movement of the conductor or circuit. Faraday’s

law considers the flux integration surface to be whatever is traced out by the move-

ment of the conductor or circuit. This avoids incorrect reasoning processes, such as

claiming in the question Q6 that there is no magnetic flow due to field B being parallel

to the circuit formed by the wire and the wall of the magnet. Some examples of this

type of answer are given below:

If the angled formed by the surface area created by the spiral and the magnetic field is

maintained constantly perpendicular, the flux will be continuously 0 and therefore no

emf will be induced as the variation of flux over time will also be 0. (First-year engineer-

ing, Q6)

The flux across the area S of the circuit C that the wire completes is: FB =∮�B · d�S in our

case �B ⊥ d�S � �B · d�S = 0 � FB = 0. So there will be neither variation in flux nor

electromagnetic induction phenomenon. There will be a current, as magnetic field B

exerts a force on the charges that are moved with velocity v; �F = q(�v× �B). (Third-year

physics, Q6)

The ammeter does not show a current, due to the fact that the disk is turning around its

axis. For the ammeter to mark a value, a velocity v should exist that would move this disk

and thereby give a variation in flux. (First-year engineering, Q7)

As B is constant, despite the fact that the disk is turning, there will be no change of flux

and therefore no induction either. There will be current along the tangent due to the

rotation and not along the radial which is what the ammeter measures. (Third-year

physics, Q7)

6.1 Students’ ideas about the role played by the magnetic field in EMI phenomena

The majority of the first-year and third-year students responded within the ‘variation

of flux’ category to the questions Q1–Q4. Students reasoned using Faraday’s law.

They used the concepts associated with the law correctly, showing a good macro-

scopic comprehension of EMI in familiar situations in the academic context. There

was a majority trend to reason based on this law, even when they did not reason cor-

rectly as for the questions Q5–Q7 (‘incorrect analysis of flux change’ category). This

result is significantly better than the one reported by Bagno and Eylon (1997), who,

during research into knowledge of electromagnetism with final-year secondary school

Israeli students, found that only 10% mentioned magnetic field variation as a cause of

induced emf. This discrepancy might be attributed both to the level of education at

which our study was run – university level – because our students had studied

more physics and to the sample of university students, which is a selected subsample

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of secondary school students. However, it is necessary to point out that more than

three-quarters of the university students did not know how to explain the nature of

the forces which move the induced current charges in the questions Q3 and Q4.

We will analyse this difficulty in the next section.

A significant percentage of the answers given by the first-year engineering and third-

year physics students to the questions Q1–Q3 revealed confusion regarding the role

played by the magnetic field in producing induced emf. More than 20% of the

first-year students’ answers explained induced current or emf as being due to the mag-

netic field in that area or space. In the case of physics students, the percentage was

little more than 16%. The following are the examples of this sort of answer included

in the ‘presence of magnetic field’ category:

When the current circulates through the upper loop, this will create a magnetic field

which will cross the lower loop and generate induced current. (First-year engineering

student, Q1)

When the magnet approaches the loop, the ammeter will record an intensity which will

depend on the field created by the magnet. If the magnet is far away the current will

hardly pass through the loop and the latter will reach its maximum when the magnet

comes closest to it. (Third-year physics student, Q3)

The standard type of answer in this category reasoned as if the field lines crossing the

loop are the cause of the induced emf. The students had analysed the cause of induced

emf in class; however, a significant percentage of the students insisted on the main

issue being that the magnetic field lines reach the loop. For example, one first-year

student wrote for the question Q2 that ‘The magnetic field lines cross the loops, indu-

cing a current’.

This reasoning is repeated for the question Q7 in about 10% of the answers. For

example:

The ammeter will register a current as there is a magnetic field at right angles to a rotating

disc, due to this there are field lines which cross it. (Third-year physics students, Q7)

In the ‘presence of magnetic field’ category, the students’ reasoning had a tendency to

attribute the cause of induced emf to the magnetic field and to confuse field lines

which cross the loop with the variation in magnetic flux through the loop. These dif-

ficulties remind us of the documented tendency of first-year university students to

confuse magnetic flux with the amount of magnetic field that ‘flows’ through an

area and their failure to understand time variation in magnetic flux (Meng Tong &

Gunstone, 2008; Saarelainen et al., 2007; Saglam & Millar, 2005).

6.2 Difficulties in Reasoning in Terms of the Forces Acting During EMI

Many of the students who answered the questions Q3 and Q4 revealed a lack of

understanding of the forces which act on the electrons in the loop in order to

produce induced electric current. Fewer than 10% of the first-year students correctly

explained the forces which act on the charges in both questions. Between 13% and

27% of the third-year physics students answered in a similar manner.

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The question Q3 required students to explain that the variable magnetic field

induces a non-conservative electric field which exerts an electric force on the electrons

in the loop. However, most of the students avoided answering in terms of the forces

intervening on the electrons (microscopic level) and spoke of variation in magnetic

flux (macroscopic level) (Table 1). This cannot be due to the way the question was

asked as it explicitly asked for an answer in terms of active forces. For example, a

first-year student wrote that:

The magnet generates a magnetic field, as the magnet moves towards the loop a large

number of force lines in the loop come in. This causes an increase in flux in the loop.

Therefore, the loop generates an induced current to maintain a constant flux.

Many answers (68% for first-year students and 33% for third-year students) were

consistent with this reasoning in terms of field. However, only a minority (4% for

first-year students and 27% for third-year students) reasoned in terms of the forces

which act on the electrons at a microscopic level. This may be attributed to most of

the students not knowing, or not applying in this situation, the ratio laid down by

one of Maxwell’s laws between a variable magnetic field and the generation of a

non-conservative field. For example, one of the third-year students who answered

in the ‘magnetic force acting’ category explained that:

When the magnet gets nearer a variation in the magnetic field is caused at the points of the

loop and, as we have studied in Maxwell’s equations, this variation in the magnetic field

causes a non-conservative magnetic field.

Similar results were obtained for the question Q4 (Table 2). To be precise, 66% of the

answers from first-year students and 64% from third-year students explained the

phenomenon in terms of the variation in the magnetic flux in the loop during a

period of time. The frequency with which this type of reasoning appeared in the ques-

tions Q3 and Q4 suggests that most of the university students had not acquired a

model of EMI which allowed them to explain it in terms of the forces acting on the

charges at a microscopic level.

6.3 Students’ Understanding of Faraday’s Law in the Phenomena of Motional emf

When answering the questions Q5–Q7, about half of the students’ answers were

included in the ‘incorrect analysis of flux change’ category. The students reasoned

wrongly regarding the variation in flux through the disc. For example, many wrote

that:

There is no induction as the magnetic field is constant and when the conductor is moved

at constant speed, the number of field lines that it crosses is always the same. There is no

change in magnetic flux. (First-year engineering student, Q5)

There will be no induction in the wire as, although it is moving, it does not enclose the

magnetic field. (First-year engineering student, Q6)

Magnetic field B and the surface area of the dS circuit are perpendicular so the resulting

flux is zero. There is no induction. (Third-year physics student, Q6)

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The ammeter will not record correctly due to the disc rotating around its axis. In order for

the ammeter to record a reading there should be a speed v which will move that disc and

thus there will be a variation in flux. (First-year engineering student, Q7)

B being constant, despite the disc rotating, there will be no change in flux because the

surface of the disc does not vary within the magnetic field. Therefore there is no induc-

tion. (Third-year physics student, Q7)

A qualitative and strict explanation of a correct interpretation of Faraday’s law is pre-

sented in the article by Layton and Simon (1998), which shows the need to consider

the integration area as the surface swept by the mobile circuit during a period of time.

However, a significant number of students’ answers fall into the ‘incorrect analysis of

flux’ category, where the students tended to consider the area appearing in the vari-

ation in flux as the area of the circuit and not the area swept by the movement of

the circuit or of the mobile part of the circuit. This means that students tended to

confuse the area of the circuit with the integration area in Faraday’s law. This

caused them to draw incorrect conclusions when predicting EMI phenomena, as

shown in the questions Q5–Q7.

6.4 Persistent Students’ Difficulties

Many of the mistakes made by the students which we have described were found for

similar answers at both teaching levels. Only 4% of the first-year students used Lor-

entz’s law to explain the force which acts on the electrons in the question Q4. We

found somewhat better percentages (about 20%) in the case of the question about

‘Faraday’s unipolar generator’ (Q7), but they were a long way from answers that

might have been expected from university students. Similarly, the differences

between the first-year and the third-year students were not as wide as might have

been expected, thus confirming that there is an on-going difficulty in learning

about an interpretative model of electromagnetic phenomena described in terms of

the effects of the field (microscopic level). Although Lorentz’s law is clearly explained

in the preceding subject on magnetic fields and forces, the learning which might be

expected has not been achieved.

The on-going difficulty in identifying the forces at work in induction was shown in

the interviews held with six first-year engineering students and 12 third-year physics

students when they were asked about the question Q4. As shown by points 7 and 8 of

the following dialogue between a third-year physics student (S) and an interviewer

(E), the explanation in terms of magnetic flux does not necessarily imply that the

nature of the forces acting on the electrons was known:

1. E: Is there a current in this experiment (question Q4)?

2. S: Yes

3. E: Could you justify your answer?

4. S: Because the flux crossing the loop is different

5. E: What makes the flux vary?

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6. S: The angle of the surface of the loop varies over the field lines. By knowing how the

flux varies, deriving it over time, we could get the reading for the induced electromotive

force.

7. E: Explain where the forces acting on the charges moving in the loop come from. What

sort of forces are we talking about? Are they forces associated with a magnetic or electric

field or . . .?

8. S: It is an electromotive movement force. I suppose that if there is an electric current it

is associated with an electric field, as in an electric circuit.

Moreover, most students’ incorrect reasoning (‘incorrect analysis of flux change’ cat-

egory), confusing the area of the circuit with the area swept by it when applying Fara-

day’s law in the case of the question Q7, should be stressed. There is no positive

progression throughout traditional teaching for this confusion. This is demonstrated

by the following dialogue from an extract of the interview held with a third-year

physics student on this question:

1. E: Is an electric current produced in this experiment (question 4)?

2. S: I don’t think so. Because the magnetic flux through the disc does not vary. Then the

derivative from the flux over time is zero as the flux is constant. There is no electromotive

force unless the magnetic field varies with time. We have said here that it is constant, so

the electromotive force induced is zero.

3. E: I don’t think you’re very sure

4. S: The fact is that we were shown a video in class with a dynamo similar to the exper-

iment in question 4 and you could see that current was passing through, but I can’t

explain it. Actually, the same number of field lines pass through because you are not

moving the disc. Then there is no variation in flux, but . . . I don’t know . . .

The results obtained showed that many answers applied Faraday’s law mechanically,

thus proving the equation’s lack of meaning to the students. As the literature shows

(see Section 2; Mauk & Hingley, 2005; Meng Thong & Gunstone, 2008; Venturini

& Alber, 2002), this kind of mechanical application of a formula with a lack of con-

ceptual understanding is typical of instruction that focuses on producing quantitative

answers to textbook problems and does not focus on conceptual understanding.

Another difficulty of the on-going difficulties throughout teaching was shown by a

significant constant of explanations which considered that induced emf is due to the

presence of a uniform magnetic field (‘presence of magnetic field’ category). This type

of explanation is similar to the results reported by Maunk and Hingley (2005) and

Meng Thong and Gunstone (2008) in previous studies. Here too, the results were

not as good as expected. For example, in the interview with a first-year engineering

student about the question Q4:

108. E: In this case, will the ammeter measure intensity?

109. S: Yes

110. E: How would you justify your answer?

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111. S: Because there is a magnetic field that crosses the coil. . . . there will be a magnetic

field inside the coil and this will generate a current.

7. Discussion

There are several common elements in the questions and the description categories given

above. All questions depict situations in which EMI is associated with a time-variable

magnetic field or with the movement of a conductor or circuit in a time-constant mag-

netic field. Thus, the most complete understanding involves a consideration of Faraday’s

law at a macroscopic level and Lorentz’s law at a microscopic level. The description

categories given in the previous section reflect these two levels of explanations and

their similarities and differences. For all questions, there is at least one description cat-

egory involving consideration of the nature of the magnetic field or surface related to

Faraday’s law. In almost all questions calling for a microscopic level of explanation,

there is a description involving Lorentz’s force. So, in each question, there is one category

which contains all the elements corresponding to an expert understanding of the

problem. In Table 3, the description categories are divided into three levels.

Level A contains explanations that consider the concepts included in Faraday’s law

and correct or incorrect understanding of them to explain the situation. Level B

includes explanations at a microscopic level and the correct use of Lorentz’s force.

As shown in Table 3, the majority of students avoided explaining EMI phenomena

in terms of the forces which act on the electrons (microscopic level) and spoke of a

variation in magnetic flux (macroscopic level). The high frequency with which this

tendency appears in all questions and in the two university courses suggests that

most students did not understand an EMI model that enabled this to be explained

in terms of field (macroscopic level) and in terms of actions exerted by the field on

the electrons (microscopic level). When students were explicitly required to explain

EMI microscopically (Q3 and Q4), only a minority of 4% of explanations achieved

this in the first year and around 20% in the third year. When the situations were fam-

iliar in the academic context for a microscopic explanation (questions Q5 and Q7),

the percentage increased, but remained far below what was expected for these

levels of instruction. However, when the students analysed experiments on EMI in

movement for situations that were not analysed explicitly in the teaching (Q6 and

Q7), the vast majority tended to confuse the circuit area with the integration area

in Faraday’s law (incorrect reasoning in level A).

The remaining explanations fall into level C. All level C explanations include badly

assimilated rote learning. For example, a significant percentage of the answers

reasoned as if magnetic field lines which cross a circuit are the cause of an induced

emf being produced and confused field lines which cross the circuit with the variation

in magnetic flux through the circuit. Other answers showed the use of concepts and

formulas without meaning. Many of the answers in this category followed incorrect

forms of reasoning already demonstrated in our previous studies on the area of elec-

tromagnetism (Guisasola et al., 2008). These findings have important teaching impli-

cations, which are discussed below.

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Table 3. Categories for answers to all questions

Description categories

Percentages of answers in category type

Q1 Q2 Q3 Q4 Q5 Q6 Q7

First Third First Third First Third First Third First Third First Third First Third

A. Explicit and correct use of Faraday’s law at

macroscopic level

49 70 58 78 68 33 66 64 25 7 4 0 7 0

Incorrect analysis of Faraday’s law 0 0 0 0 0 0 0 0 25 33 45 57 41 47

B. Explanations using electromagnetic forces at

microscopic level

0 0 0 0 4 27 4 13 21 31 0 0 20 20

C. Badly applied rote learning 47 30 32 21 22 35 18 20 16 22 24 18 28 22

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8. Implications for Physics Teaching

When drawing conclusions and implications for teaching, it is necessary to bear in

mind that the questionnaire and interviews were carried out with a small number of

students at a single university. Thus, we cannot produce evidence for more general

contexts. Our study has not been designed to present conclusive evidence on all uni-

versity students’ difficulties with learning about EMI and, in fact, there may be diffi-

culties due to other factors not explicitly taken into account in this study. However, we

have checked that the results obtained in this study match results found in other

studies carried out with student samples from other countries (Galili et al., 2006;

Layton & Simon, 1998). Furthermore, the results obtained present new features

which showed that a significant percentage of the students cannot interpret simple

induction phenomena properly. It is not enough to give simple problems such as

the questions Q1, Q2, and Q5 describe above, find that the majority of students are

able to describe an appropriate explanation, and conclude that the majority of the

class ‘understand EMI’. All we can say is that in the simpler questions (Q1 and

Q5), most students used Faraday’s law correctly.

As in any situation, EMI can be explained macroscopically and microscopically,

and we have to consider that different situations are treated differently depending

on the context. Our data show that this does not happen; the students have a majority

tendency to explain the phenomena of induction with macroscopic concepts and laws,

including in situations (Q4–Q7) where reasoning is based on Lorentz’s law, and

microscopically, it considerably facilitates the analysis of the induction phenomenon.

Thus, teachers must not only teach based on straightforward transfer of concepts and

laws with illustrations of ad hoc examples, but also specify the key points of the model

on which students must reflect and be guided to understand phenomena.

The data reported here reflect the value of questions, such as Q3–Q7, which

require qualitative answers when demonstrating deep understanding of physics con-

cepts and laws. As shown in Table 3, a major difference in students’ responses is

evident between simple standard questions and questions which ask for understand-

ing at the macro and micro levels. Teachers cannot afford to ignore the importance of

students being able to deal with fundamental concepts in different contexts. The

results of this study show that it is necessary to emphasise explaining the macroscopic

aspects (in terms of field) and the microscopic aspects (in terms of field actions) of the

model and to justify that one or other may be used indiscriminately to explain EMI. It

is clear that when it is a case of a conductor moving in a constant magnetic field over

time, the explanation in terms of active field forces is simple and useful, whereas for

other phenomena, the use of the variation in magnetic flux through an area (in terms

of field) is simpler. However, the key aspect for reflection with students is why one

explanation or another is chosen and, in any event, it should be made clear that

both are acceptable for any situation.

In future work, it will be necessary to clarify teaching–learning objectives, taking

into account students’ alternative conceptions and appropriate teaching methods.

An approach based on presenting problems and developing tutor-led research to

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resolve them seems a priori suitable for designing teaching materials to make students

think about the key aspects that are being referred to (Lijnse & Klaasen, 2004). Other

research has chosen the benefits of considering key aspects of the physical theory

(Guisasola, Zubimendi, & Zuza, 2010; Lindsey, Heron, & Shaffer, 2009). Training

students how to reflect on the key aspects of the model is important for them to under-

stand and apply it. We suggest that research into this approach which designs didactic

materials and implements them with students is necessary in order to reduce the gap

between teaching EMI and students understanding it.

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Appendix: Questionnaire

Q1. When the switch on the upper circuit in the diagram is turned off, it is found

experimentally that ammeter G on the lower circuit registers a current. Explain in

detail why a current appears in the lower circuit.

Q2. In the diagram below, you can see details of a solenoid that is crossed by a mag-

netic field. Do you think that magnetic induction occurs? Explain your answer in

detail.

Q3. We have a magnet which moves towards a conducting loop which is at rest as

we look at it (see figure); at any time as it moves closer, the ammeter registers a current

through the conducting wire loop. As you have learnt, the electric current in the loop

is due to an electrical force associated with an induced electric field. Explain how this

electric field appears in the loop and the nature thereof.

Q4. When changing the direction of the loop, it is found experimentally that

ammeter G in the loop registers a current. Explain where the forces which move

the charges in the loop come from and the nature thereof.

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Q5. A metal bar such as that shown in the diagram is immersed in a region where

there is a stationary magnetic field B directed inside the sheet; an instant initial force is

applied that makes this bar move to the right with speed v. In these conditions:

(a) Would the magnetic induction phenomenon occur in this bar?

(b) If so, how would you explain the appearance of this phenomenon?

Q6. A U-shaped wire is sliding along a magnet as shown in the figure maintaining

its angle to the magnetic field. Bearing in mind that both the wire and the magnet are

conductors, is there an induction phenomenon in the wire? Justify your answer.

Q7. The figure shows a copper disc rotating within a uniform magnetic field at right

angles to it. We want to know whether an induced emf will be produced in this situ-

ation and to do so an ammeter is placed between the centre of the disc and the outer

part of the rotating disc. Will the ammeter register a current?

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