**Introduction **

Electromagnetic induction (EMI) is a challenging topic for students (see [1] and references therein for education research on this area). I recall that as a student, I had an uneasy feeling about it. While I could do most of the questions I faced, I wasn’t happy with the topic the way I was with, say, gravitational fields. I remember learning about many diverse phenomena, whose behaviour was explained in terms of changes of magnetic flux (Faraday’s ‘flux rule’). Yet I didn’t see why flux had to necessarily be invoked when a wire cut across magnetic field lines, nor why pushing a magnet into a coil induced a current. Sure, the ‘flux rule’ was meant to explain the latter, but it didn’t seem to explain (to me at least) why electrons would start moving in the coil on account of the magnet’s motion.

Such memories returned to me when I started tutoring a few years ago. With my first A-level physics tutee, I followed a textbook presentation of EMI. Although the student did very well, I wasn’t satisfied with the way I taught the material. From our discussions, I saw that the student grappled with many of the problems I faced as a student. I started thinking of an alternative presentation, which I arrived at after some research, and which I would like to discuss in this article.

A summary of this presentation is:

*It may be helpful to present EMI in terms of three different types of induction, rather than viewing all induction phenomena in terms of the ‘flux rule’. *

It’s possible to understand all of EMI in terms of the ‘flux rule’; see for instance the comprehensive notes by Kirk McDonald [2]. However, there are phenomena where this is not at all obvious; even the Feynman lectures [3] famously discuss a number of examples which appear to violate the universality of the ‘flux rule’. One such example is the Faraday disk dynamo, variants of which often turn up in questions, and which I’ll examine below. The point is, that while it is possible to understand all of EMI in terms of the ‘flux rule’, this is unlikely to be helpful to the novice. This suggests that the topic be presented in such a way that makes explicit the different types of induction, thus enabling students to better organise their understanding.

The ideas discussed in this article are not new: the concept of different types of EMI has long been appreciated. For instance, in the research literature, [4] refers to two types of induced emf (‘transformer’ and ‘motional’), while [5] talks of three different kinds of EMI. However, I am unaware of the exact presentation below being discussed previously in any resource or literature.

The three different types of EMI that I’ve alluded to above are:

– Type I: ‘Cutting field lines’

– Type II: ‘Flux changes in a loop’

– Type III: ‘Overlap’ (of type I and type II)

I’ll discuss each of these in turn below; the figures shown below originate from a series of youtube videos that I’ve created on EMI [6]. I’ll then analyse some possible issues with this presentation and finally conclude.

**Type I: ‘Cutting field lines’ **

This type of induction is typically how the topic is introduced: a conductor cuts perpendicularly across magnetic field lines. Conduction electrons, upon experiencing a magnetic force–the direction of which can be predicted from Fleming’s left hand rule (FLHR)–move to one end of the conductor, thereby creating an induced emf. This is shown in the figure below.

At this point, presentations will often quickly move on to the concept of magnetic flux and the ‘flux rule’ [7, 8]. This quick transition may potentially confuse students, and may also represent a ‘lost opportunity’ in the following sense: the discussion above demonstrates that students would already have met the required concepts (in magnetism), to understand why an induced emf would develop.

The concept of magnetic flux is not needed here (and needn’t be mentioned), and so this is an opportunity for students to learn new concepts while reinforcing old ones e.g. FLHR. Furthermore, one could introduce Faraday’s law of induction (emf = Blv), and perhaps refer to it as Faraday’s law for ‘cutting field lines’. This formula is often derived from considering the ‘flux rule’, but it doesn’t have to be–see simple proof here [8] which makes no reference to flux.

One potential benefit of presenting different types of induction is that it opens the possibility to discussing key concepts such as Lenz’s law from different angles. This allows students to ‘take several bites’, and thereby strengthen understanding. The above ‘cutting field lines’ scenario can be extended to discuss ideas of energy conservation, work and Lenz’s law. FLHR can be used again to deduce a downward opposing magnetic force acting on the conductor, as shown in the figure below.

As well as not requiring magnetic flux, the above discussion shows that the key to understanding ‘cutting field lines’ is the magnetic force and FLHR. Fleming’s right hand rule (FRHR) or the ‘dynamo rule’ is often used instead. In my opinion, we can do away with FRHR entirely to simplify our presentation: FRHR becomes an unnecessary thing that students have to learn, and introduces the possibility of students getting mixed up between Fleming’s hand rules. FLHR encodes a physical principle (the magnetic or Lorentz force), whereas FRHR is just an ad hoc rule, as far as I can tell.

A possible drawback of the above approach is that students often find the notion of a downward current due to the conductor moving up a bit abstract at first; indeed, I’ve found this to be the case in my tutoring. This is compounded by the induced current that develops (along the conductor) and the idea of applying FLHR separately to these two currents. However, with enough practice I don’t see this as being insurmountable.

A real practical benefit of discussing ‘cutting field lines’ as described above is when it comes to the Faraday disk dynamo (FDD). See the figure below.

Variations on the FDD often turn up in questions, for example, electromagnetic braking systems. In my experience, students often struggle with such questions due to their conceptual nature. They mostly fall back on stock answers to do with the ‘flux rule’. Yet if one looks at the disk rotating in a magnetic field in the figure above, there doesn’t appear to be any changes of magnetic flux! It turns out that one can interpret the FDD in terms of flux changes (see section 2.4.1 in [2]), however this is far beyond what would be expected of an A-level physics student. Moreover, interpreting the FDD in terms of flux changes obscures the simplicity of the phenomenon. A more physically transparent interpretation is to view the FDD as an instance of ‘cutting field lines’. We can view the disk as being composed of many strips or sectors (such as the one highlighted in blue in the figure), that cut across the magnetic field lines as the disk rotates. One can then proceed to discussions about FLHR, Lenz’s law etc. just as before.

Understanding that the FDD is an example of ‘cutting field lines’ is not obvious to the novice–it’s something that needs to be explicitly pointed out. The FDD shows the benefits of students being taught about ‘cutting field lines’ as a distinct type of induction, where no reference is made to magnetic flux, and the fundamental role of the magnetic force is impressed on them. The importance of the magnetic force in EMI appears not to be emphasised much in existing A-level presentations.

**Type II: ‘Flux changes in a loop’ **

This type of induction, as the name suggests, calls for explicit reference to magnetic flux. The simplest example of this is when a bar magnet is pushed towards or away from a wire loop, as shown in the figure below.

To make it clear to students that this type of induction should be viewed as being distinct from type I, it’s important to choose examples where the conductor is stationary. (Personally, I don’t think it’s worthwhile getting into reasoning based on relativity either, since students aren’t acquainted with such ideas.) Given the discussion about magnetism and FLHR for type I, I’ve found that students naturally try to interpret the above scenario using those ideas. Having the conductor stationary is important in order to make the point that there is no ‘cutting field lines’ going on and that therefore, the induced emf is not due to the magnetic force. For discussions about AC generators, instead of considering a rotating coil, one can simply consider a fixed coil and a rotating magnet. Depending on one’s familiarity with electromagnetism, it may be worth discussing briefly that a changing magnetic field gives rise to an electric field, which is what’s responsible for the induced emf in these phenomena. At any rate, I know that I would have enjoyed learning about this when I was doing my A-levels! See the figure below.

When introducing Faraday’s ‘flux rule’, one could refer to it as Faraday’s law for ‘flux changes in a loop’, to contrast it with Faraday’s law for ‘cutting field lines’. One can revisit Lenz’s law during the course of discussing this second type of induction.

**Type III: ‘Overlap’ (of type I and type II) **

The third type of induction is what I’ve termed the ‘overlap’ (of types I and II). Naturally, this concerns phenomena which can be viewed either in terms of type I or type II. The classic example of this is when a conducting rod slides along a fixed ‘U-shaped’ conductor with a magnetic field acting perpendicular to the area bounded by the circuit, as shown in the figure below.

Starting from the ‘flux rule’, one can show that Faraday’s law for ‘cutting field lines’ can be derived, thus showing the equivalence of the two ways of looking at the problem. Hopefully this shouldn’t come as a great surprise to students; by this stage, they will possibly notice themselves that there’s elements of type I and II in the scenario. One can then discuss the issue of which formula (version of Faraday’s law) to use. Either one works, but the choice is usually determined by matters of convenience i.e. what information is given and which choice involves the least amount of work.

Another example of type III induction is an AC generator, with a fixed magnetic field but rotating coil, in contrast to the AC generator mentioned above in type II. A related concept is back emf for motors. If one decides to discuss this, one can appeal to the magnetic force and FLHR (as discussed in type I) to explain how the magnetic force diminishes the electrical current as the coil spins. This provides a simple and transparent explanation of back emf.

**Possible issues with the presentation **

There are a number of objections one may raise about this presentation of EMI. One is that it’s perhaps too time consuming. Not being in a position to test this out in a classroom, this isn’t something I can comment on. Another objection is that this approach may be too challenging for the typical student. Certainly, it is demanding, but then again, EMI in itself is challenging–in my opinion the most demanding topic in school physics. The tutees (of various abilities) that I’ve had a chance to discuss these ideas with seemed to appreciate it; it appeared to help clarify their thinking. I find it hard to see how one can justify the transition from a conductor ‘cutting field lines’ to changes of magnetic flux (mentioned in type I), which appears to be the typical presentation. It seems to me that a more layered approach is likely to be more beneficial.

Another objection may be that most questions on induction involve magnetic flux, and that this justifies spending the majority of time discussing flux. This is a fair point, but as I’ve argued above in discussing the FDD, just concentrating on flux is unlikely to prepare students for the full variety of questions that they may encounter. They are also unlikely to build a coherent understanding of the underlying concepts of EMI. Also, the amount by which I’ve discussed the various types of induction in this article shouldn’t be interpreted as reflecting how much time should be spent proportionally teaching the different types. For instance, for type II, time would need to be spent discussing preparatory concepts (such as flux) and a variety of the many examples of type II.

One may also be rather uneasy about teaching ideas that aren’t strictly true i.e. the inability of the ‘flux rule’ to explain all EMI phenomena. Teaching physics (especially at pre-university level) is a trade-off between simplicity and accuracy. As students progress, they have a chance to refine and update their understanding, by unlearning ‘partial truths’. I believe the relative transparency of the above presentation outweighs any concerns regarding its inaccuracy.

There are likely to be other issues which I’ve overlooked, and I look forward to learning about these from feedback.

**Summary **

In this article, I’ve discussed the possible benefits of presenting the topic of EMI in terms of three different types of induction, rather than exclusively in terms of Faraday’s ‘flux rule’. Such a partition ought to help students better organise their understanding and feel more confident about the topic. Armed with this framework, students would have the ability to spot which class of induction a particular problem falls into, and thus better negotiate some of the trickier questions, such as variants of the FDD. By explicitly referring to two versions of Faraday’s law (emf = Blv and the ‘flux rule’), students may better appreciate when it is appropriate to use either formula, by virtue of understanding what type of induction is present in a phenomenon.

**References **

[1] Jelicic, K., Planinic, M., & Planinsic, G. (2017). Analyzing high school students’ reasoning about electromagnetic induction. *Physical Review Physics Education Research*, *13*(1), 010112.

[2] McDonald, K. T. (2019). Is Faraday’s Disk Dynamo a Flux-Rule Exception? http://kirkmcd.princeton.edu/examples/faradaydisk.pdf

[3] R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics, Vol. 2, sec. 17-2 (Addison Wesley, 1964), http://www.feynmanlectures.caltech.edu/II_17.html

[4] Galili, I., Kaplan, D., & Lehavi, Y. (2006). Teaching Faraday’s law of electromagnetic induction in an introductory physics course. *American journal of physics*, *74*(4), 337-343.

[5] Roche, J. (1987). Explaining electromagnetic induction: a critical re-examination. The clinical value of history in physics. *Physics Education*, *22*(2), 91.

[6] https://www.youtube.com/playlist?list=PL6rr9avuArH4dQaHntn6B8ByJE0QhpGl3 [7] Breithaupt, J. (2016). *AQA Physics: A Level Year 2*. Oxford University Press-Children. [8] https://spark.iop.org/episode-414-electromagnetic-induction

*Featured photo by Mika Baumeister on Unsplash*