Electromagnetic induction — using the LEFT hand rule…?

They do observe I grow to infinite purchase,
The left hand way;

John Webster, The Duchess of Malfi

Electromagnetic induction — the fact that moving a conductor inside a magnetic field in a certain direction will generate (or induce) a potential difference across its ends — is one of those rare-in-everyday-life phenomena that students very likely will never have come across before. In their experience, potential differences have heretofore been produced by chemical cells or by power supply units that have to be plugged into the mains supply. Because of this, many of them struggle to integrate electromagnetic induction (EMI) into their physical schema. It just seems such a random, free floating and unconnected fact.

What follows is a suggested teaching sequence that can help GCSE-level students accept the physical reality of EMI without outraging their physical intuition or appealing to a sketchily-explained idea of ‘cutting the field lines’.

‘Look, Ma! No electrical cell!’

I think it is immensely helpful for students to see a real example of EMI in the school laboratory, using something like the arrangement shown below.

A length of copper wire used to cut the magnetic field between two Magnadur magnets on a yoke will induce (generate) a small potential difference of about 5 millivolts. What is particularly noteworthy about doing this as a class experiment is how many students ask ‘How can there be a potential difference without a cell or a power supply?’

The point of this experiment is that in this instance the student is the power supply: the faster they plunge the wire between the magnets then the larger the potential difference that will be induced. Their kinetic energy store is being used to generate electrical power instead of the more usual chemical energy store of a cell.

But how to explain this to students?

A common option at this point is to start talking about the conductor cutting magnetic field lines: this is hugely valuable, but I recommend holding fire on this picture for now — at least for novice learners.

What I suggest is that we explain EMI in terms of a topic that students will have recently covered: the motor effect.

This has two big ‘wins’:

  • It gives a further opportunity for students to practice and apply their knowledge of the motor effect.
  • Students get the chance to explain an initially unknown phenomenon (EMI) in terms of better understood phenomenon (motor effect). The motor effect will hopefully act as the footing (to use a term from the construction industry) for their future understanding of EMI.

Explaining EMI using the motor effect

The copper conductor contains many free conduction electrons. When the conductor is moved sharply downwards, the electrons are carried downwards as well. In effect, the downward moving conductor can be thought of as a flow of charge; or, more to the point, as an electrical current. However, since electrons are negatively charged, this downward flow of negative charge is equivalent to an upward flow of positive charge. That is to say, the conventional current direction on this diagram is upwards.

Applying Fleming Left Hand Rule (FLHR) to this instance, we find that each electron experiences a small force tugging it to the left — but only while the conductor is being moved downwards.

This results in the left hand side of the conductor becoming negatively charged and the right hand side becoming positively charged: in short, a potential difference builds up across the conductor. This potential difference only happens when the conductor is moving through the magnetic field in such a way that the electrons are tugged towards one end of the conductor. (There is, of course, the Hall Effect in some other instances, but we won’t go into that here.)

As soon as the conductor stops moving, the potential difference is no longer induced as there is no ‘charge flow’ through the magnetic field and, hence, no current and no FLHR motor effect force acting on the electrons.

Faraday’s model of electromagnetic induction

Michael Faraday (1791-1867) discovered the phenomenon of electromagnetic induction in 1831 and explained it using the idea of a conductor cutting magnetic field lines. This is an immensely valuable model which not only explains EMI but can also generate quantitative predictions and, yes, it should definitely be taught to students — but perhaps the approach outlined above is better to introduce EMI to students.

The left hand rule not knowing what the right hand rule is doing . . .

We usually apply Fleming’s Right Hand Rule (FRHW) to cases of EMI, Can we replace its use with FLHR? Perhaps, if you wanted to. However, FRHR is a more direct and straightforward shortcut to predicting the direction of conventional current in this type of situation.

Split ring commutator? More like split ring commuHATER!

Students find learning about electric motors difficult because:

  1. They find it hard to predict the direction of the force produced on a conductor in a magnetic field, either with or without Fleming’s Left Hand Rule.
  2. They find it hard to understand how a split ring commutator works.

In this post, I want to focus on a suggested teaching sequence for the action of a split ring commutator, since I’ve covered the first point in previous posts.

Who needs a ‘split ring commutator’ anyway?

We all do, if we are going to build electric motors that produce a continuous turning motion.

If we naively connected the ends of a coil to power supply, then the coil would make a partial turn and then lock in place, as shown below. When the coil is in the vertical position, then neither of the Fleming’s Left Hand Rule (FLHR) forces will produce a turning moment around the axis of rotation.

When the coil moves into this vertical position, two things would need to happen in order to keep the coil rotating continuously in the same direction.

  • The current to the coil needs to be stopped at this point, because the FLHR forces acting at this moment would tend to hold the coil stationary in a vertical position. If the current was cut at this time, then the momentum of the moving coil would tend to keep it moving past this ‘sticking point’.
  • The direction of the current needs to be reversed at this point so that we get a downward FLHR force acting on side X and an upward FLHR force acting on side Y. This combination of forces would keep the coil rotating clockwise.

This sounds like a tall order, but a little device known as a split ring commutator can help here.

One (split) ring to rotate them all

The word commutator shares the same root as commute and comes from the Latin commutare (‘com-‘ = all and ‘-mutare‘ = change) and essentially means ‘everything changes’. In the 1840s it was adopted as the name for an apparatus that ‘reverses the direction of electrical current from a battery without changing the arrangement of the conductors’.

In the context of this post, commutator refers to a rotary switch that periodically reverses the current between the coil and the external circuit. This rotary switch takes the form of a conductive ring with two gaps: hence split ring.

Tracking the rotation of a coil through a whole rotation

In this picture below, we show the coil connected to a dc power supply via two ‘brushes’ which rest against the split ring commutator (SRC). Current is flowing towards us through side X of the coil and away from us through side Y of the coil (as shown by the dot and cross 2D version of the diagram. This produces an upward FLHR force on side X and a downward FLHR force on side Y which makes the coil rotate clockwise.

Now let’s look at the coil when it has turned 45 degrees. We note that the SRC has also turned by 45 degrees. However, it is still in contact with the brushes that supply the current. The forces on side X and side Y are as noted before so the coil continues to turn clockwise.

Next, we look at the situation when the coil has turned by another 45 degrees. The coil is now in a vertical position. However, we see that the gaps in the SRC are now opposite the brushes. This means that no current is being supplied to the coil at this point, so there are no FLHR forces acting on sides X and side Y. The coil is free to continue rotating clockwise because of momentum.

Let’s now look at the situation when the coil has rotated a further 45 degrees to the orientation shown below. Note that the side of the SRC connected to X is now touching the brush connected to the positive side of the power supply. This means that current is now flowing away from us through side X (whereas previously it was flowing towards us). The current has reversed direction. This creates a downward FLHR force on side X and an upward FLHR force on side Y (since the current in Y has also reversed direction).

And a short time later when the coil has moved a total of180 degrees from its starting point, we can observe:

And later:

And later still:

And then:

And then eventually we get back to:

Summary

In short, a split ring commutator is a rotary switch in a dc electric motor that reverses the current direction through the coil each half turn to keep it rotating continuously.

A powerpoint of the images used is here:

And a worksheet that students can annotate (and draw the 2D versions of the diagrams!) is here:

I hope that this teaching sequence will allow more students to be comfortable with the concept of a split ring commutator — anything that results in a fewer split ring commuHATERS would be a win for me 😉

Explaining current flow in conductors (part three)

Do we delve deeply enough into the actual physical mechanism of current flow through electrical conductors using the concepts of charge carriers and electric fields in our treatments for GCSE and A-level Physics? I must reluctantly admit that I am increasingly of the opinion that the answer is no.

In part one we discussed two common misconceptions about the physical mechanism of current flow, namely:

  1. The all-the-electrons-in-a-conductor-repel-each-other misconception; and
  2. The electric-field-of-the-battery-makes-all-the-charge-carriers-in-the-circuit-move misconception.

In part two we looked at how the distribution of surface charges on electrical conductors produces the internal electric fields that guide and push charges around electric circuits and highlighted the published evidence that supports this model.

A representation of a surface charge distribution giving rise to the internal electric field (purple arrows) of a current-carrying conductor

In part three, we are going to look at the transient processes that produce the required distribution of surface charges. In this treatment, I am going to lean very heavily on the analysis presented in Duffin (1980: 167-8).

Connecting wires to a chemical cell

Let’s connect up a simple circuit using a chemical cell as our source of EMF ℰ.

The first diagram shows the cell and wires before they are connected.

When the wires are connected there is a momentary current flow from the cell that creates the surface charge distribution shown below.

The current will stop when the ends of the wire at a potential difference V which is equal to the EMF ℰ of the cell. The ends of the wire act as a small capacitor (∼10-15 F or less). The wires act as equipotential volumes so the very small charge must be distributed over the surface of the wires with a slight concentration of charge at the ends.

Making the circuit

If the ends of the wire are now connected, then the capacitance drops to zero and the ends of the wires become discharged. This leads to very low concentration of surface charge in this region.

However, just enough surface charge remains to produce the internal electric field as shown below. The field lines of the internal electric field are parallel to the wire.

The potential diagram is after Figure 6.17 (Duffin 1980: 160). The ‘dip’ between C and A is due to the effect of the internal resistance of the cell. As we can see in this instance, when there is a steady flow of current then V is slightly smaller than ℰ.

Reference

Duffin, W. J. (1980). Electricity and magnetism (3rd ed.). McGraw Hill Book Co

Whoa, black body (bam-ba-lam): part two

In part one, we looked at the fact that the hotter an object then the greater the intensity of electromagnetic radiation that will be emitted. For simplicity, we looked at so-called ‘blackbodies’ — that is say, objects which are perfect absorbers (hence ‘blackbodies’) and more importantly, perfect emitters of electromagnetic radiation.

To human eyes, things look very dull in the visible part of the electromagnetic spectrum until we reach temperatures of several hundreds of degrees — however, objects at room temperature (or just above) glow brightly in the infrared part of the electromagnetic spectrum, as we can see easily if we have access to an infrared camera.

By ‘intensity’ of course, we mean the power (‘energy per second’) emitted per unit area.

This links in neatly with 4.6.3.2 of the 2015 AQA GCSE Physics specification:

Stretch and challenge for students (1): Is the intensity of emitted radiation directly proportional to the temperature of the object?

The short answer is no. If you doubled the temperature (measured in kelvins!) of an object then the intensity of radiation would increase by a factor of 16. In other words, the intensity I of radiation emitted by an object is directly proportional to the absolute temperature T raised to the power of 4.

This is a consequence of the Stefan-Boltzmann radiation law (covered in A-level Physics):

In part 1 we estimated the intensity of radiation emitted by two blackbodies by ‘counting squares’ to find the area underneath a graph. We can show that the values obtained are consistent with the Stefan-Boltzmann radiation law.

Since we have dealt comprehensively with the relationship between intensity of radiation and temperature, I propose to move along and look at how the wavelength distribution changes with the temperature of the body.

How does the temperature of a blackbody affect the distribution of emitted wavelengths?

Let’s consider an object that approximates to a blackbody: the filament of an old school incandescent lamp.

The graph of the radiation produced by both objects is shown below.

First, let’s look at the visible wavelengths produced by both bulbs.

  • The 1700 degree Celsius bulb produces only a very small amount of visible light and the vast majority of that is towards the red end of the spectrum: you can see the section where the left hand edge of the 1700 curve just nicks the visible light wavelengths. This means that the 1700 degree filament emits a barely perceptible reddish glow to our eyes with its peak output still firmly in the infrared.
  • The 2200 degree Celsius bulb produces a much larger amount of visible light: look at the left hand side of the curve. What is more, it appears as white light to our eyes since it includes all the colours of the rainbow. However, it’s still a very reddish-tinged white. Photographs taken in artificial light with chemical films (very old school!) had to be taken using special colour balanced film stock otherwise this bias was very evident in the final print(!) Modern digital cameras have software that automatically compensates for artificial vs. daylight colour balance issues.

Second, let’s look at the position of the peak wavelength.

  • The 1700 degree Celsius bulb has its peak output at a wavelength of 1.5 x 10-6 m (shown by the blue dotted line on the graph).
  • The 2200 degree Celsius bulb has its peak output at a wavelength of 1.2 x 10-6 m (shown by the red dotted line on the graph.)

Assuming that you wanted to, these findings could be summarised in song (sung to the tune of ‘Black Betty’ by Ram Jam):

Whoa, black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)
More heat, peak shifts left
Waves out with more zest
Wavelengths out not alike
Some hues power spike!
Whoa, black body (Bam-ba-lam)
Whoa, black body 
Bam-ba-laaam, yeah yeah
 

Stretch and challenge for students (2): predicting the position of the peak output wavelength

The position of the peak output wavelength can be predicted using Wien’s Displacement Law (studied in A-level Physics:

As we can see, the peak output wavelength on the graph agrees well with the position as calculated by Wien’s Displacement Law.

An unannotated pdf of the graph can be downloaded here:

Whoa, black body (bam-ba-lam)

The 2015 AQA GCSE Physics specification (4.6.3.1) asks that students understand that:

In my experience, students find it natural to accept that bodies absorb electromagnetic radiation — but surely only extremely hot objects (like the filament of a light bulb) emit electromagnetic waves?

This is a consequence of the fact that our eyes can only detect the tiny slice of the vast electromagnetic spectrum.

That tiny sliver known as ‘visible light’ looks insultingly small even on a diagram with a logarithmic scale as shown above. On a linear scale, it’s even worse: if we represented the em spectrum by a line stretching from London to New York, then the range of wavelengths that human eyes can detect would be a strip two centimetres wide.

This calls to my mind some lines quoted many years ago by Arthur C. Clark in his wonderful essay ‘Things We Cannot See’: A being who hears me tapping / The five-sensed cane of mind / Amid such greater glories / That I am worse than blind.

Seeing the unseeable

A Leslie’s cube is a cuboid with black and silver coloured faces that can filled with hot water.

In visible light, there is no difference between its appearance when at room temperature (say 15 degrees Celsius) and when filled with hot water (say 70 degrees Celsius).

However, seen through an infrared camera, things look very different: the hot sides glow brightly, emitting huge amounts of infrared em waves.

There is another effect: the black coloured side throws out more infrared than the silver side. Why? Because any object which is good at absorbing em radiation is also good at emitting radiation.

As the AQA GCSE spec puts it:

By this definition, the Sun is a good approximation of a black body since it absorbs nearly all of the radiation falling on it (from other stars! — as well as the odd photon bounced back from minuscule specks like the Earth) as well being highly effective at emitting em radiation.

Black body radiation curves

4.6.3.2 of the AQA GCSE Physics spec says:

One of the ways to cover this is to look at the radiation curves of two black bodies at different temperatures (pdf here). Both of these objects are at relatively low temperatures, so they emit most of their energy in the infrared part of the em spectrum. The visible light range is shown by the coloured bar just to the right of the y-axis.

Because it is a perfect emitter — as well as absorber — of radiation, the intensity (power per unit area) of emitted radiation from a black body depends only on the temperature of the black body.

Estimating the total power emitted per unit area

We can estimate the total power emitted per unit area by approximating the area underneath the curve. We’re going to count any square which is larger than a half square as one whole square and ignore any part squares which are smaller than a half square.

The area under the blue curve is 325 W/m^2.

The intensity of radiation emitted by the hot object (red curve) is larger than the intensity emitted by the cold object (blue curve).

You can download an unannotated pdf copy of the graph by clicking on the link below.

We will look at the distribution of wavelengths in a later post.

Whoa, black body (bam-ba-lam)

Physics can occasionally, go better with a song.

Whoa, black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)
Black body e.m. waves (Bam-ba-lam)
Come out with peak shapes (Bam-ba-lam)
Planck said, “I’m worryin’ outta mind (Bam-ba-lam)
UV won’t align!” (Bam-ba-lam)
He said, oh black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)

Whoa, black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)
Planck set out to Quantise (Bam-ba-lam)
UV don’t catastrophize! (Bam-ba-lam)
Theory rock steady (Bam-ba-lam)
“No prob now,” said he (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)

Get it!

Whoa, black body (Bam-ba-lam)
Whoa, black body (Bam-ba-lam)
More heat, peak shifts left
Waves out with more zest
Wavelengths out not alike
Some hues power spike!
Whoa, black body (Bam-ba-lam)
Whoa, black body 
Bam-ba-laaam, yeah yeah

(with apologies to Huddie Ledbetter)

Make choo choo go faster

Captain Matthew Henry Phineas Riall Sankey sighed and shaded his tired eyes from the bright glare of the oil lamp. Its light reflected harshly from the jumbled mounds of papers that entirely covered the dark oak surface of his desk. He took a moment to roll down the wick and dim the light. The chaos of his work area hinted at the chaos currently roiling in his usually precise and meticulous engineer’s mind.

He leaned backward in his chair, his shoulders slumped in despair. This problem had defeated many other men before him, he reflected as he stroked his luxuriant moustache: there would be no shame in admitting defeat.

After all, he was only one man and he was attempting to face down the single most serious and most pressing scientific and engineering issue known to the world in the Victorian Era. And yet — he couldn’t help but feel that he was, somehow, close to solving it. The answer seemed to hover mirage-like in front of him, almost within his grasp but blurred and indistinct. It became as insubstantial as mist each time he reached for it. He needed a fresh perspective, a new way of looking simultaneously both at the whole and at the parts of the question. It was not so much a question of not seeing the wood for the trees, but rather seeing the wood, trees, twigs and leaves in sufficient detail at the same time.

And what was this problem that was occupying the finest scientific and technical minds at the close of the nineteenth century? It was simply this:

Make choo choo go faster

You think I jest. But no: in 1898 the world ran on the power of steam. Steam engines were the shining metal giants that laboured tirelessly where hundreds of millions of men and beasts had toiled in misery before. In less enlightened times, industry had rested on the backs of living things that strained and suffered under their load; now. however, it was built on the back of machines that felt no pain and could work day and night when fed with coal.

So much progress had been made over the years from the clanking primitive behemoths pioneered by Thomas Newcomen and James Watt. Those wasteful old engines had always teetered far too close to the edge of scalding catastrophe for comfort and demanded the tribute of a mountain of coal for a miserly hillock of work.

Modern steam engines were sleeker, safer and more efficient. But they still demanded too much coal for a given amount of work: somewhere, deep within their intricate web of moving parts, energy was wastefully haemorrhaging. No matter how much coal you loaded into the firebox or how hotly it burned, the dreadful law of diminishing returns worked its malevolent magic: the engine would accelerate to a certain speed, but no faster, no matter what you did. You always got less work out than you put in.

Captain Henry Phineas Sankey was searching for a tourniquet that would stem the malign loss of energy in the innards of these vital machines. He could not help but think of the wise words written by Jonathan Swift many long years ago:

Whoever could make two ears of corn, or two blades of grass, to grow upon a spot of ground where only one grew before, would deserve better of mankind, and do more essential service to his country, than the whole race of politicians put together.

What Captain Henry Phineas Sankey hoped to do was nothing less than reverse engineer the venerable Jonathan Swift: whereas previously a steam engine would burn two tons of coal to perform a task, he wanted to build an engine that would do the same work by burning only one ton of coal. That he hoped would be his enduring memorial both of his service to his country and to mankind.

But how to achieve this? How could one man hold in his head the myriad moving, spinning parts of a modern steam engine and ascertain how much loss there was here rather than there, and whether it was better to try and eliminate the loss here which might increase the weight of that particular part and hence lead to an unavoidably greater loss over there . . .

Captain Sankey’s restless eyes alighted on a framed drawing on the wall. It had been painstakingly drawn some years ago by his son, Crofton, and then delicately painted in watercolours by his daughter, Celia, when they were both still very young children. They had both been fascinated by the story of Napoleon’s ill-fated Russian Campaign of 1812. The drawing showed Charles Minard’s famous map of 1869.

It showed the initial progress of Napoleon’s huge army as a wide thick band as they proudly marched towards Moscow and its gradual whittling down by the vicissitudes of battle and disease; it also showed the army’s agonised retreat, harried by a resurgent Russian military, and fighting a constant losing battle against the merciless ‘General Winter’. Only a few — a paltry, unhappy few — Frenchmen had made it home, represented by the sad emaciated black line at journey’s end.

Mrs Eliza Sankey had questioned allowing their children to spend so much time studying such a ‘horrible history’ but Captain Sankey had encouraged them. Children should not only know the beauties of the world but also its cruelties, and everyone should attend to the lesson that ‘Pride goeth before a fall’.

The map showed all of that. It was not just a snapshot, but a dynamic model of the state of Napoleon’s army during the whole of the campaign: from the heady joys of its swift, initial victories to its inevitable destruction by cruel attrition. It was a technical document of genius, comparable to a great work of art, for it showed not only the wood but the trees and even the twigs all at one time . . .

Captain Sankey started suddenly. He had an idea. Unwilling to spare even an instant in case this will ‘o the wisp of an idea disappeared, he immediately clipped a blank sheet of paper to his drawing board. He slid the T-square into place and began to draw rapidly. This is the work that Captain wrought:

Later that evening, he wrote:

No portion of a steam plant is perfect, and each is the seat of losses more or less serious. If therefore it is desired to improve the steam plant as a whole, it is first of all necessary to ascertain separately the nature of the losses due to its various portions; and in this connection the diagrams in Plate 5 have been prepared, which it is hoped may assist to a clearer understanding of the nature and extent of the various losses.

The boiler; the engine; the condenser and air-pump; the feedpump and the economiser, are indicated by rectangles upon the diagram. The flow of heat is shown as a stream, the width of which gives the amount of heat entering and leaving each part of the plant per unit of time; the losses are shown by the many waste branches of the stream. Special attention is called to the one (unfortunately small) branch which represents the work done upon the pistons of the engine

Captain Sankey (1898)

The ubiquitous Sankey diagram had been born . . .

How NOT to draw a Sankey diagram for a filament lamp

Although this diagram draws attention to the ‘unfortunately small’ useful output of a filament lamp, and it is still presented in many textbooks and online resources, it is not consistent with the IoP’s Energy Stores and Pathways model since it shows the now defunct ‘electrical energy’ and ‘light energy’.

Note that I use the ‘block’ approach which is far easier to draw on graph paper as opposed to the smooth, aesthetically pleasing curves on the original Sankey diagram.

How to draw a Sankey diagram for a filament lamp

We can, however, draw a similar Sankey diagram for a filament lamp that is completely consistent with the IoP’s Energy Stores and Pathways model if we focus on the pathways by which energy is transferred, rather than on the forms of energy.

The second diagram, in my opinion, provides a much more secure foothold for understanding the emission spectrum of an incandescent filament lamp.

And, as the Science National Curriculum reminds us, we should seek to use ‘physical processes and mechanisms, rather than energy, to explain’ how systems behave. Energy is a useful concept for placing a limit on what can happen, but at the school level I think it is sometimes overused as an explanation of why things happen.

Closing thought

Stephen Hawking surmised that humanity had perhaps 100 years left on a habitable Earth. We are in a race to make a less destructive impact on our environment. ‘Reverse engineering’ Swift’s ‘two ears of corn where one grew before’ so that one joule of energy would do the same work as two joules did previously would be a huge step forward.

And for that goal, the humble Sankey diagram might prove to be an invaluable tool.

Helping Students With Extended Writing Questions in Science

Part one: general principles

He knew all the tricks: dramatic irony, metaphor, pathos, puns, parody, litotes* and . . . satire. He was vicious.

Monty Python, The Tale of the Pirhana Brothers

As we all know, students really struggle with questions in science exams which require answers written ‘at paragraph length’ (dread words!). What follows are some tips that I have found useful when coaching students to improve performance.

Many teachers of English enjoy great success with acronyms such as PEEL (Point. Example. Explain. Link). However, I think these have limited applicability in Science as the required output of extended writing questions (EWQs) varies too much for even a loose one-size-fits-all approach.

What I encourage students to do is:

1. Write in bullet points

The bullet points (BPs) should be short but fully grammatical sentences (and not single words or part sentences).

The reason for this is twofold:

  • Focus: it stops an attempted answer spiralling out of control. Without organising my answer using BPs, I find myself running out of space. I start with the best of intentions but realise, as I fill in the last remaining line of the allocated space, that I haven’t reached the end of the first sentence yet!!!
  • Organisation: it discourages students from repeating the same thing again and again. I have sometimes marked extended writing answers that repeat the same point multiple times. Yes, they have filled the space and yes, they have written in complete sentences. But there is no additional information except the first section rewritten using different words!

2. Use correct scientific vocabulary

Students often make the incorrect assumption that ‘Explain‘ means ‘Explain to a non-specialist using jargon-free everyday language‘.

In fact nothing could be further from the truth. The expectation of EWQs in general is that students should be able to communicate to a scientist-peer using technical language appropriate for GCSE or A-level.

Partly, this misconception is our own fault. When students ask for an explanation from their teachers, we often — with the best of intentions! — try to express it in non-threatening, jargon-free language.

This is the model that many students follow when responding to EWQs. For example, I remember groaning in frustration when marking an A-level Physics script where the student has repeatedly written the word ‘move’ when the terms ‘accelerate’ or ‘constant velocity’ would have communicated her understanding with far more clarity.

In Science, what is often derided as ‘jargon’ isn’t an actual barrier to understanding. In truth, a shared, specialist language is an essential pathway to concision and clarity and a guard-rail against inadvertent miscommunication.

3. Write as many BPs as there are marks

For example, students should aim to write 3 BPs in response to a 3-mark EWQ.

4. Read all your BPs. Taken as a whole — do they *answer* the damn question?

If yes, move on. If no, then add another BP.


Part two: modelling the EWQ response-process

‘What does “quantum” mean, anyway?’

‘It means “add another nought.”‘

Terry Pratchett, Pyramids

This EWQ has 3 marks, so we should aim for 3 BPs.

I use the analogy of crossing a river using stepping stones. One stepping stone won’t be enough but three will let us get across — hopefully without us getting our feet wet.

Let’s write our first BP. I suggest that students begin by stating what they may think is obvious.

Next, we think about what we could write as our second BP. But — and this is essential! — we consider it from the vantage point of our first BP.

Our second BP is the next-most-obvious-BP: what happens to the solenoid when an electric current goes through it? Remember that we are supposed to use technical language, so we will call a solenoid a solenoid, so to speak.

Next, we consider what to write for our third (and maybe final) BP. Again, we should be thinking of this from the viewpoint of what we have already written.

Finally, and this point is not to be missed, we should look back at all the BPs we have written and ask ourselves the all-important ‘Have I actually answered the question that was asked originally?

In this case, the answer is YES, we have explained why the door unlocks when the switch is closed.

This means that we can stop here and move on to the next question.


*Litotes (LIE-tote-ees): an ironic understatement in which an affirmative is expressed as a negative e.g. I won’t be sorry to get to the end of this not-at-all-overlong blog post.

The Apparatus of Golgi: Science As It Should Be

Carl Sagan said that science is unique in having it’s own built-in error correcting machinery:

The scientific way of thinking is at once imaginative and disciplined. This is central to its success. Science invites us to let the facts in, even when they don’t conform to our preconceptions [ . . .] One of the reasons for its success is that science has built-in, error correcting machinery at its very heart. Some may consider this an overbroad characterization, but to me every time we exercise self-criticism, every time we test our ideas against the outside world, we are doing science. When we are self-indulgent and uncritical, when we confuse hopes and facts, we slide into pseudoscience and superstition.

Sagan 1997: 35 [emphasis added]

Of course, scientists are only human, and are sometimes as susceptible to self-indulgence and reluctance to criticise their own “pet” theories as the next person. But not always.

Richard Dawkins (2006) shares the following story about the reaction of a highly respected “elder statesman” of science to evidence countering his long-held opinion about a structure inside living cells called the Apparatus of Golgi (GOL-jee).

An animal cell. The Apparatus of Golgi is labelled 6. For other labels, click on the link https://en.wikipedia.org/wiki/Golgi_apparatus

I have previously told the story of a respected elder statesman of the Zoology Department at Oxford when I was an undergraduate [c.1960]. For years he had passionately believed, and taught, that the Golgi Apparatus (a microscopic feature of the interior of cells) was not real: an artefact, an illusion. Every Monday afternoon it was the custom for the whole department to listen to a research talk by a visiting lecturer. One Monday, the visitor was an American cell biologist who presented completely convincing evidence that the Golgi Apparatus was real. At the end of the lecture, the old man strode to the front of the hall, shook the American by the hand and said — with passion — “My dear fellow, I wish to thank you. I have been wrong these fifteen years.” We clapped our hands red.

Dawkins 2006: 283

References

Dawkins, R. (2006). The God Delusion. Bantam Press.

Sagan, C. (1997). The Demon-Haunted World: Science As A Candle In The Dark. Random House Digital, Inc

Using dimensional analysis to estimate the energy released by an atomic bomb

Legend has it that in the early 1950s, British physicist G. I. Taylor was visited by some very serious men from the military authorities. His crime? He had apparently secured unauthorised access to worryingly accurate and top secret information about the energy released by the first atom bomb.

Sir G. I. Taylor (1896-1965)

Taylor explained that, actually, he hadn’t: he had estimated the energy yield from a series of photographs of the first atomic test explosion published by Life magazine. Taylor had used the standard physics technique known as dimensional analysis.

Part of the sequence of photographs of the Trinity atomic weapon test (16/7/45) published by Life magazine in 1950

The published pictures had helpfully included a scale to indicate the size of the atomic fireball in each photograph and Taylor had been able to complete a back-of-the-envelope calculation which gave a surprisingly accurate value for what was then the still highly classified energy yield of an atomic weapon.

This story was shared by the excellent David Cotton (@NewmanPhysics) on Twitter, and included a link to a useful summary which forms the basis of what follows. (NB Any errors or omissions are my own.)

It is presented here for A-level Physics teachers to consider using as an example of the power of dimensional analysis beyond the usual “predicting the form of the equation for the period of a simple pendulum”(!)

Taylor’s method: step one

Taylor began by assuming that the radius R of the fireball would depend on:

  • The energy E released by the bomb. The larger the energy released then the larger the fireball.
  • The density of the air ρ. The greater the density of the air then the smaller the fireball since more work would have to be done to push the air out of the path of the fireball.
  • The time elapsed t from the explosion. The longer the time then the larger the size of the fireball (until the moment when it began to collapse).

These three factors can be combined into a single relationship:

k is an unknown arbitrary constant. Note that we would expect the exponent y to be negative since R is expected to decrease as ρ increases. We would, however, expect x and z to be positive.

Taylor’s method: step two

Next we think of the dimensions of each of the values in terms of the basic dimensions or measurements of length [L], mass [M] and time [T].

  • R has the dimension of length, so R = [L].
  • E is in joules or newton metres (since work done = force x distance). From F=ma we can conclude that the dimensions of newtons are [M] [L] [T]-2. This makes the dimensions of energy [M] [L]2 [T]-2.
  • ρ is in kilograms per cubic metre so it has the dimensions [M] [L]-3.
  • t has the dimension of time [T].

Taylor’s method: step three

Next we write equation 1 in terms of the dimensions of each of the quantities. We can ignore k as we assume that this is a purely numerical value with no units. This gives us:

Simplifying this expression, we get:

Taylor’s method: step four

Next, let’s look at the exponents of [M], [L] and [T].

Firstly, we can see that x + y = 0 since there is no [M] term on the left hand side.

Secondly, we can see that 2x – 3y = 1 since there is an [L] term on the left hand side.

Thirdly, we can see that z – 2x = 0 since there is no [T] term on the left hand side.

Taylor’s method: step five

We now have a system of three equations detailing three unknowns.

We can solve for x, y and z using simultaneous equations. This gives us x=(1/5), y=(-1/5) and z=(2/5).

Taylor’s method: step six

Let’s rewrite equation 1 using these values. This gives us:

Rearranging for E gives us:

Taylor’s method: step seven

Next we read off the value of t=0.006 s and estimate R=75 m from the photograph. The density of air ρ at normal atmospheric pressure is ρ=1.2 kg/m3.

If we substitute these values into equation 6 (assuming that k=1) we get E= 7.9 x 1013 joules.

Conclusion

Modern sources estimate the yield of the Trinity test as being equivalent to between 18-20 kilotons of TNT. Let’s take the mean value of 19 kilotons. One kiloton is equivalent to 4.184 terajoules. This means that, according to declassified sources that were not available to Taylor, the energy released by the Trinity test was 7.9 x 1013 joules.

As you can see, Taylor’s “guesstimated” value using the dimensional analysis technique was remarkably close to the actual value. No wonder that the military authorities were concerned about this apparent “leak” of classified information.

Explaining current flow in conductors (part two)

Do we delve deeply enough into the actual physical mechanism of current flow through electrical conductors using the concepts of charge carriers and electric fields in our treatments for GCSE and A-level Physics? I must reluctantly admit that I am increasingly of the opinion that the answer is no.

In part one we discussed two common misconceptions about the physical mechanism of current flow, namely:

  1. The all-the-electrons-in-a-conductor-repel-each-other misconception; and
  2. The electric-field-of-the-battery-makes-all-the-charge-carriers-in-the-circuit-move misconception.

What, then, does produce the internal electric field that drives charge carriers through a conductor?

Let’s begin by looking at the properties that such a field should have.

Current and electric field in an ohmic conductor

(You can see a more rigorous derivation of this result in Duffin 1980: 161.)

We can see that if we consider an ohmic conductor then for a current flow of uniform current density J we need a uniform electric field E acting in the same direction as J.

What produces the electric field inside a current-carrying conductor?

The electric field that drives charge carriers through a conductor is produced by a gradient of surface charge on the outside of the conductor.

Rings of equal charge density (and the same sign) contribute zero electric field at a location midway between the two rings, whereas rings of unequal charge density (or different sign) contribute a non-zero field at that location.

Sherwood and Chabay (1999): 9

These rings of surface charge produce not only an internal field Enet as shown, but also external fields than can, under the right circumstances, be detected.

Relationship between surface charge densities and the internal electric field

Picture a large capacity parallel plate capacitor discharging through a length of high resistance wire of uniform cross section so that the capacitor takes a long time to discharge. We will consider a significant period of time (a small fraction of RC) when the circuit is in a quasi-steady state with a current density of constant magnitude J. Since E = J / σ then the internal electric field Enet produced by the rings of surface charge must be as shown below.

Schematic diagram showing the relationship between the surface charge density and the internal electric field

In essence, the electric field of the battery polarises the conducting material of the circuit producing a non-uniform arrangement of surface charges. The pattern of surface charges produces an electric field of constant magnitude Enet which drives a current density of constant magnitude J through the circuit.

As Duffin (1980: 167) puts it:

Granted that the currents flowing in wires containing no electromotances [EMFs] are produced by electric fields due to charges, how is it that such a field can follow the tortuous meanderings of typical networks? […] Figure 6.19 shows diagrammatically (1) how a charge density which decreases slowly along the surface of a wire produces an internal E-field along the wire and (2) how a slight excess charge on one side can bend the field into the new direction. Rosser (1970) has shown that no more than an odd electron is needed to bend E around a ninety degree corner in a typical wire.

Rosser suggests that for a current of one amp flowing in a copper wire of cross sectional area of one square millimetre the required charge distribution for a 90 degree turn is 6 x 10-3 positive ions per cm3 which they call a “minute charge distribution”.

Observing the internal and external electric fields of a current carrying conductor

Jefimenko (1962) commented that at the time

no generally known methods for demonstrating the structure of the electric field of the current-carrying conductors appear to exist, and the diagrams of these fields can usually be found only in the highly specialized literature. This […] frequently causes the student to remain virtually ignorant of the structure and properties of the electric field inside and, especially, outside the current-carrying conductors of even the simplest geometry.

Jefimenko developed a technique involving transparent conductive ink on glass plates and grass seeds (similar to the classic linear Nuffield A-level Physics electrostatic practical!) to show the internal and external electric field lines associated with current-carrying conductors. Dry grass seeds “line up” with electric field lines in a manner analogous to iron filings and magnetic field lines.

Photograph from Jefimenko (1962: 20). Annotations added

Next post

In part 3, we will analyse the transient processes by which these surface charge distributions are set up.

References

Duffin, W. J. (1980). Electricity and magnetism (3rd ed.). McGraw Hill Book Co.

Jefimenko, O. (1962). Demonstration of the electric fields of current-carrying conductorsAmerican Journal of Physics30(1), 19-21.

Rosser, W. G. V. (1970). Magnitudes of surface charge distributions associated with electric current flow. American Journal of Physics38(2), 265-266.

Sherwood, B. A., & Chabay, R. W. (1999). A unified treatment of electrostatics and circuits. URL http://cil. andrew. cmu. edu/emi. (Note: this article is dated as 2009 on Google Scholar but the text is internally dated as 1999)