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Revolutions in Physics Notes
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REVOLUTIONS IN PHYICS
ELECTROMAGNETISM AND SPACE-TIME
1. Introduction
One of the most exciting things in Physics is to discover relationships between observed effects (or
phenomena) that were previously thought to be quite distinct. What happened in electromagnetism in
the nineteenth century is a wonderful example. In the year 1800 there were only the vaguest
indications that magnetism had anything to do with moving electric charges, and no evidence at all
that light had anything to do with electricity or magnetism. By 1900 magnetism and electricity had
been firmly linked, and light had been shown to be an electromagnetic wave. How this came about,
sometimes in small steps, and sometimes by seemingly bizarre lines of reasoning, is the subject of this
option.
In one respect the new theory that linked electricity, magnetism and light seemed not to agree with the
facts, as found in experiments. In 1905 Einstein’s Special Theory of Relativity came to the rescue. At
the same time, it actually simplified the theory of electromagnetism (and light). Included in this option
there is a small taste of Relativity theory.
2. Questions and answers about this option
Q What is the point of studying this option?
A • It reinforces some of the non-optional A-Level material, coming at it from a different angle,
giving it a wider context, and adding ‘human interest’.
• It brings the student into contact with great minds and great ideas.
• Sheer self-indulgence – it’s a wonderful story.
Q
A
Q
A
Q
A
Q
A
How can the material presented in this option, derived from what others have written, give the
promised ‘contact with great minds’?
A few extracts from some of the key figures (Young, Faraday, Maxwell and Einstein) are
provided. The extracts are not very long, but are to be studied closely. Guidance is given.
Does the student have to learn dates?
No, but having the right half-decade is good. In fact people often ‘absorb’ dates easily when
there’s a chain of events – and when there’s no stress to learn dates!
What has to be left out in order to fit the story into an A-level option?
This is a real problem. Looking back on past events and ideas, it’s easy to see, or to think we see,
which of them led nowhere or were of secondary importance, and to leave them out. But at the
time they may have been considered very important. They may have influenced the way physicists
thought, in ways we cannot now know. By omitting them we distort history. Please be aware that
this option cannot tell the whole story.
Can anything be done to give a more balanced picture?
Websites references are sprinkled throughout this WJEC material. Two thinnish and very
readable books which provide good support are…
Michael Faraday and the Royal Institution by John Meurig Thomas (ISBN 0-7503-0145-7).
Relativity and its Roots by Banesh Hoffmann (ISBN 0-486-40676-8).
Chapter 4 tells pretty much the same story as this course, but, as the book’s title makes clear,
Hoffmann has a special agenda, and his emphases are different.
All the material to be tested in the PH5 examination is contained in this WJEC printed
material, but students are urged to visit the websites, as they help to bring the basic
material of the option alive and make it easier to learn. They often contain pictures and
diagrams.
3. Electricity, Magnetism and Light: What was known in 1800
3.1 Electric Charge
• It had been known from ancient times that objects, in particular lumps of amber, could be
‘charged’ by rubbing, and could sometimes attract attract or repel other objects. [Our word
electricity comes from the greek word for amber.]
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• Around 1730, Stephen Gray (www.sparkmuseum.com/BOOK_GRAY.HTM) had found that damp
thread, and metals, would conduct charge from one object to another, whereas many materials
were insulators (when dry). [Charge was often referred to as ‘electricity’ and charging, as
‘electrifying’.]
• Soon after, it emerged that there were two sorts of electric charge, and that these could neutralise
each other. Some years later, the american statesman and scientist, Benjamin Franklin, called them
positive and negative. Amber gains a negative charge when rubbed with fur; glass, a positive,
when rubbed with silk.
• Franklin showed, by extremely dangerous experiments, that thunder clouds contain electric charge,
and
that
lightning
is
an
electrical
phenomenon.
(www.inventors.about.com/cs/inventorsalphabet/a/Ben_Franklin_4.htm )
• In about 1745 Dutch investigators discovered that opposite charges could be stored on conducting
surfaces coating the inside and the outside of a glass bottle, and so separated by the insulator, glass.
The device quickly came to be called a Leyden jar, after Leyden, now Leiden, in the Netherlands. It
was used in demonstrations all over Europe to produce sparks and electric shocks - and much
excitement.
• In the late 1780s, Coulomb (www.en.wikipedia.org/wiki/Charles_Augustin_de_Coulomb ) made the
first quantitative investigation of the forces between charged spheres. These were of small enough
diameter, in relation to their separation, to be considered ‘point charges’. Using a torsion balance of his
own devising, he showed that there was an inverse square law, that is, when the separation of the
centres of the spheres was doubled, the force between the spheres quartered, and so on.
(http://library.thinkquest.org/C001429/electricity/electricity11.htm )
[The reclusive Henry Cavendish had made the same discovery some years earlier, but did not publish
his findings.]
Coulomb and his contemporaries were struck by the similarity between this inverse square law for
charges and Newton’s inverse square law of gravitation for masses.
3. Electricity, Magnetism and Light: What was known in 1800
3.2 Magnetism
In the year 1800, most of the knowledge about magnetism dated from 1600, when William Gilbert
had published his great work De Magnete (‘About the Magnet’). He described his experiments to
magnetise iron bars using a lodestone (naturally occurring magnetised iron ore), reported on the
‘magnets’ having poles at either end (the word ‘poles’ is his), and found that even if you cut a magnet
in half, each of the two halves still had both a North and a South pole. He investigated the effect of the
Earth on a pivoted magnet, and came to the conclusion that the Earth itself was a magnet. He
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demolished many superstitions about magnetism, but we would regard his own view as to the cause of
magnetic effects as very odd. (http://galileo.rice.edu/sci/gilbert.html )
Although the attraction and repulsion behaviour of magnetic poles resembles that of electric charges,
Gilbert was very careful to explain that magnetic and electric effects were quite distinct.
3.3 The Battery
This was hot news in the year 1800. Back in the 1780s, Luigi Galvani had observed the twitching of a
leg cut from a dead frog, when a nerve was touched by a piece of metal which was also in contact
with the foot. The effect, he found, was much greater if two different metals were joined together.
There are various versions of how the discovery was made; see for example
www.bioanalytical.com/info/calendar/97/galvani.htm . Galvani attributed the twitching to ‘animal
electricity’, perhaps in the frog’s nerves.
Alessandro Volta took up the investigation and became convinced that it was the different metals
which played the key role. He devised a cell consisting of a strip of zinc and a strip of copper dipping
into a cup of brine or dilute acid, but not touching each other, and then started putting cells in series
(as we would now say). Two forms of ‘battery’ emerged, the ‘crown of cups’
(www.scienceandsociety.co.uk/results.asp?image=10207373 ) and the famous ‘voltaic pile’
(www.en.wikipedia.org/wiki/Voltaic_pile ). [In French the name still survives: une pile or une pile
electrique is a battery.]
News of Volta’s invention spread quickly, and batteries, sometimes very large ones, were built all
over Europe and in America. They were found to melt wires, connected across their terminals, and to
enable the splitting up of water up into oxygen and hydrogen. Some investigators were nearly killed
by
electric
shocks
from
batteries
of
many
cells.
Humphry
Davy
(www.rigb.org/rimain/heritage/ripeople/davy.jsp ), at the recently founded ‘Royal Institution’ in
London, used batteries to perform electrolyses which isolated sodium, potassium and various other
elements for the first time. He also fascinated audiences with demonstrations of what a battery could
do.
Davy’s audiences weren’t made up entirely, or even mainly, of people we would now call ‘scientists’.
Any intelligent person – with the leisure – could contribute to a scientific debate. Davy himself was
quite a gifted poet and was a friend of Wordsworth and Coleridge. There wasn’t really an ‘artsscience divide’. ‘Galvanism’, the term used then for the study of the battery and what it could do, was
much talked about, and we might guess that it was one of the influences on the young Mary Shelley,
when she was writing Frankenstein (published in 1818).
Volta himself had established a connection between batteries and electric charge. He discovered that
the terminals of his batteries were charged positively and negatively. Charge collected from the
terminals could be used to make bodies attract and repel, in specially designed instruments. The
battery provided for the first time the means of producing a continuous flow of charge, or electric
current. [Charge in this context was often referred to as an ‘electric fluid’, and there was controversy
over whether there were really two fluids or just one. We shan’t follow this particular sub-plot.]
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3. Electricity, Magnetism and Light: What was known in 1800
3.4 Light
In the 1660s Newton had performed a brilliant series of experiments showing that ‘white light’ was a
mixture of colours. He made other major contributions to optics. Naturally he wondered what light
was.
Newton’s rival, Robert Hooke (of Hooke’s Law fame) believed it to be a wave-like disturbance
travelling through, and by means of, a universal medium (often called the aether or ether). Christiaan
Huygens, a strong supporter of a wave theory of light, showed how to predict where a wavefront will
be, and what its shape will be, if we know its position and shape now. He gave convincing wave
theory accounts of reflection and refraction.
(http://encarta.msn.com/encyclopedia_761567208/Christian_Huygens.html )
For Newton and others, the problem with the wave theory was that light doesn’t seem to bend round
corners, for example when opaque objects are put in its path. Water waves, though, do bend and
spread into the ‘shadow’ behind obstacles, sound travels round corners – and so do Huygens’
wavefronts. For this reason, mainly, Newton could not accept that light was a wave, or, more
accurately, just a wave. He held that it consisted of a stream of corpuscles or particles, coming from
its source. But he knew there were problems with this: if light fell on a sheet of glass, some goes
through and some is reflected. Why should some corpuscles do one thing and others another?
Newton wrote of light as having ‘fits’ of easy reflection and fits of easy refraction, and hinted that
possibly some sort of wave-like disturbance might accompany the corpuscles and determine what
they did.
Such was the awe in which Newton was held for showing how an inverse square law of gravitation
accounted for the motion of the planets, the moon and the tides, that his corpuscular theory of light
was given enormous respect. If you challenged it, even long after Newton’s death, you would have to
defend yourself very convincingly.
3.5 Questions on section 3
(1) It was discovered in the 1700s that metals could be charged up by rubbing with a dry cloth. In
what special way would the metal have to be held?
(2) A leyden jar would now be classed as a sort of …………………….. ?
(3) How, mathematically, do we now write Coulomb’s inverse square law for electric charges?
(4) What, according to William Gilbert, was the ‘soul of the Earth’?
(5) In what you have read, have you come across any pre-1800 evidence for a connection between
electricity and magnetism?
(6) What was ‘galvanism’, and why was it so called?
(7) Is it true that none of the effects of an electric current could have been observed before the work
of Galvani and Volta?
(8) How does the wave theory of light account for refraction?
(9) What political upheaval was shaking Europe in the 1790s?
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4. Re-birth of the Wave Theory of Light
4.1 Thomas Young
Thomas Young (born in 1773) was a child prodigy. When four years old, he is said to have read the
bible in its entirety…twice. By the age of fourteen he had mastered several languages, ancient and
modern.
He lived up to his early promise. As a medical
student he discovered the mechanism by which
the eye focuses (or accommodates), and, at the
age of 21 was elected a Fellow of the Royal
Society. This is Britain’s most prestigious
scientific society, dating from the time of
Newton.
In 1801, when Young had set up as a doctor in
London, he was chosen as Professor of Natural
Philosophy (roughly speaking, Physics) at The
Royal Institution. [He turned out not to be as
charismatic a lecturer as Humphry Davy.]
At about this time Young started his researches
on light – see below.
Later in life he made some headway in
deciphering the ancient Egyptian heiroglyphics
on the Rosetta Stone.
www.whonamedit.com/doctor.cfm/1715.html
Writing about light, Young stated two
‘hypotheses’ ;
“A luminiferous [light-carrying] ether pervades the universe.”
“Undulations [waves!] are excited in this ether whenever a body becomes
luminous.”
He explained that:
“an undulation is supposed to consist in a vibratory motion; transmitted
successively through different parts of a medium without any tendency in each
particle to continue its motion except in consequence of the transmission of
successive undulations from a distinct vibrating body.”
Young’s new idea, apparently not grasped by Huygens, was that light had to be a regular sequence of
undulations. This implied that light from the same source, travelling to the same point by different
routes would interfere either constructively or destructively, according to phase difference. Using the
idea of interference, Young was able to explain ‘Newton’s Rings’ a phenomenon which had puzzled
Newton himself. Visit the website below for pictures – strictly ‘for interest only’!
www.physics.montana.edu/demonstrations/video/6_optics/demos/newtonsrings.html
Note that it did not occur to Young at the time that light could be anything other than a longitudinal
wave, like sound.
Young seems [historians argue about it] first to have shown a version of his famous two slits
experiment in a lecture given to The Royal Society in 1803. Here is the account he gives of such an
experiment…
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4. Re-birth of the Wave Theory of Light
4.1 Thomas Young (Continued)
“It has been shown that two equal series of waves, proceeding from centres near
each other, may be seen to destroy each other’s effects at certain points, and at other
points to redouble them; and the beating of two sounds has been explained from a
similar interference. We are now to apply the same principles to the alternate union
and extinction of colours.
“In order that the effects of two portions of light may thus be combined, it is
necessary that they be derived from the same origin, and that they arrive at the
same point by different paths in directions not much deviating from each other.
This deviation may be produced in one or both the portions by diffraction, by
reflection, by refraction, or by any of these effects combined: but the simplest case
appears to be, when a beam of homogeneous light falls on a screen in which there
are two very small holes or slits, which may be considered as centres of divergence,
from whence the light is diffracted in every direction.
“In this case, when the two newly formed beams are received on a surface placed so
as to intercept them, their light is divided by dark stripes into portions nearly equal,
but becoming wider as the surface is more remote from the apertures, so as to
subtend very nearly equal angles from the apertures at all distances, and wider also
in the same proportion as the apertures are closer to each other. The middle of the
two portions is always light, and the brighter stripes on each side are at such
distances, that the light coming to them from one of the apertures, must have
passed through a longer space than that which comes from the other, by an interval
which is equal to the breadth of one, two, three or more of the supposed
undulations, while the intervening dark spaces correspond to a difference of half a
supposed undulation, of one and a half, of two and a half, or more.
“From a comparison of various experiments, it appears that the breadth of the
undulations constituting the extreme red light must be supposed to be, in air, about
one 36 thousandth of an inch, and those of the extreme violet, about one 60
thousandth; the mean of the whole spectrum, being about one 45 thousandth. From
these dimensions it follows, calculating upon the known velocity of light, that
almost 500 millions of millions of the slowest of such undulations must enter the
eye in a single second.”
Young continues with a description of the ‘beautiful diversity of tints’ in the fringes which are seen
when white light is used. The above extract is as Young wrote it, apart from one comma being
removed and one new paragraph created. There were no diagrams (apart from the one below);
readers
were
supposed
to
…
read.
And
visualise!
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4. Re-birth of the Wave Theory of Light
4.1 Thomas Young (Continued)
Here are some must-do ‘comprehension’ questions on this first-ever description of a now famous
experiment.
(1) What did Young mean by a ‘luminiferous ether’? What purpose did it serve?
(2) Draw the set-up described by Young in the second paragraph and the beginning of the third
paragraph in the long extract. It should be familiar!
(3) What – in a word – does Young mean by ‘the breadth of an undulation’ (near the bottom of the
third paragraph)?
ay
(4) WJEC gives the ‘Young’s fringes formula’ as

.
D
(5)
(6)
(7)
(8)
(9)
(a) Re-arrange it to make the fringe separation the subject.
(b) Pick out the phrase from Young’s third paragraph in which he states the effect on the fringe
separation of altering D.
(c) Pick out the phrase from Young’s third paragraph in which he states the effect on the fringe
separation of altering a.
The bright stripe next the central bright stripe is at such a distance, to use Young’s terminology,
that the light coming to it from one of the apertures must have passed through a longer space
than that which comes from the other, by an interval which is equal to the breadth of one of the
supposed undulations. Put this in modern ‘path difference’ language.
1 inch = 2.54 cm. Hence express in metres Young’s results (fourth paragraph) for the
wavelengths of the extremes of the visible spectrum. Do they agree with what textbooks give?
What is conspicuously missing from this account of a quantitative experiment?
When, at the end of the passage, Young refers to ‘the slowest of such undulations, he means
those of the lowest frequency. What does he give as their approximate frequency?
Young refers near the end to ‘the known velocity of light’. [It had been inferred a long time
previously by two different methods based on two quite different sorts of astronomical
measurements.] Work backwards from Young’s figures for longest wavelength and lowest
frequency to deduce what figure he must have been using for the velocity of light.
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4. Re-birth of the Wave Theory of Light (Continued)
4.2 Reactions to Young
Young’s experiment is the classic demonstration that light has wave-like properties. But that is not
how it was seen at the time. Maybe Young’s contemporaries would have been more convinced if
he’d given his actual readings, and explained properly how he’d arrived at his results for
wavelengths. Then there was the long-dead Newton to contend with. How dare this upstart, Young,
challenge the great Newton’s view that light was a stream of particles?
Henry Brougham, a barrister who later rose to become Lord Chancellor, wrote an infamous review
of one of Young’s Royal Society papers. He accused Young of putting forward an (unjustified)
theory, and having to make changes to it …
“A mere theory is in truth destitute of all pretentions to merit of every kind, except
that of a warm and misguided imagination. It demonstrates neither patience of
investigation, nor rich resources of skill, nor vigorous habits of attention, nor
powers of abstracting and comparing, nor extensive acquaintance with nature. It is
the unmanly and unfruitful pleasure of a boyish and prurient imagination, or the
gratification of a corrupted and depraved appetite.
“If, however, we condescend to amuse ourselves in this manner, we have the right
to demand, that the entertainment shall be of the right sort – that the hypothesis
shall be so consistent with itself, and so applicable to the facts, so as not to require
perpetual mending and patching – that the child which we stoop to play with shall
be tolerably healthy, and not of the puny, sickly nature of Dr Young’s productions
[...]”
Not impressed, then? In another paragraph (which no writer today could expect to get away
with) Brougham accused Young of bringing the Royal Society into disrepute…
“Has the Royal Society degraded its publications into bulletins of news and
fashionable theories for the ladies who attend the Royal Institution? Proh Pudor!
[For shame!] Let the professor continue to amuse his audience with an endless
variety of such harmless trifles; but, in the name of Science, let them not find
admittance into that venerable repository which contains the works of Newton, and
Boyle, and Cavendish and Maskelyne and Herschell (sic, the correct spelling is
Herschel).” (http://homepages.wmich.edu/~mcgrew/brougham.htm for interest only!)
Brougham’s reaction was extreme, but, even putting it aside, Young’s work on interference and the
wave
theory
didn’t
attract
much
enthusiasm
at
the
time.
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4. Re-birth of the Wave Theory of Light (Continued)
4.3 Transverse waves
Real trouble soon arrived for the wave theory.
In about 1808 Etienne Malus discovered an
astonishing fact about the light reflected from
a transparent sur-face. The effect is observed
to perfection for the light reflected off a glass
plate, A, when the angle of incidence is 57°.
The reflected ray is found to be reflected from
another glass plate, B, when this is as shown
in the left hand diagram, but not when B is
turned about the ray as axis, so that it is as
shown on the right. The light must be
asymmetrical about its direction of travel! [A
related effect involving certain crystals, called
‘double refraction’, had puzzled natural philosophers for well over a century. Polaroid had
not been invented.]
To an A-level student the solution should be
obvious: light is a transverse wave, and A must be polarising it. But it hadn’t occurred to Young that
light could be anything else but a longitudinal wave, like sound. Eventually, though, (c1818) the
penny dropped.
By this time another powerful wave theorist, Augustin Fresnel, was at work in France.
(http://micro.magnet.fsu.edu/optics/timeline/people/fresnel.html ). He came upon the significance of
interference independently of Young, and developed the wave theory mathematically. He showed
convincingly that the reason we don’t normally see light bending round corners is because of its
short wavelength. He accounted for polarisation by reflection, double refraction and the diffraction
patterns caused by various obstacles. For a spherical obstacle his equations made an unlikely
prediction … (www.physics.brown.edu/physics/demopages/Demo/optics/demo/6c2010.htm )
4.4 Problems with the Ether
Fresnel effectively killed off the corpuscular theory. Most natural philosophers were persuaded that
light was a transverse wave. The only sort of wave anyone could imagine was a mechanical wave, in
which a pattern of displacements transmits itself through a medium, the ‘ether’. Try and follow this
crude and sketchy explanation…
In the diagram a transverse wave is travelling to the right. The medium is stiff, so the shaded slice
experiences an upward tangential or ‘shearing’ force from
the upwardly displaced slice to its left. The shaded slice will
accelerate upwards, and the peak displacement, P, will
move to the right – and so on.
There were severe problems with this ‘mechanical’ theory…
• It is difficult to see why the ether shouldn’t transmit
longitudinal waves as well as transverse waves. Yet no
longitudinal waves were observed.
• Transverse waves need a stiff medium, a solid, rather than a liquid or gas. But we receive sunlight
and starlight, so all space must be full of this medium. How, then can the planets move without
obstruction? Indeed, how can anything move freely?
For the next few decades, elaborate attempts were made to devise ether structures which would not
have these problems. We shall return to the ether…
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5. Discoveries in Electromagnetism
5.1 Ørsted
Electromagnetism was born in 1820 when Hans Christian Ørsted (or Oersted)
(http://en.wikipedia.org/wiki/Hans_Christian_Ørsted) discovered that a copper wire connected across
the terminals of a battery could deflect a compass needle (in other words, a pivoted magnet). The
effect was just as large if non-magnetic substances other than air were placed between the wire and
the magnet. As long as it was close enough to the wire, the magnet was deflected to be almost at
right angles to the wire. The North-seeking pole pointed in opposite directions according to whether
the magnet was below or above the wire. It seemed as if the magnet directions were tangential to
circles going round the wire.
Quick Checks
• Do the needle directions shown agree with the right hand grip (or screw) rule?
• Why does the needle have to be close to the wire to be deflected almost at right angles to the
wire? What other influence is there on the needle?
• Why won’t the experiment work if the wire runs East-West?
A Historical Puzzle
Twenty years had gone by between the invention of the battery and Ørsted’s discovery, and this is
rather odd. For one thing, there was a sort of ‘galvanism mania’ after Volta announced his invention,
and the powers of the battery were explored with great zeal. For another, there were tantalising clues
that magnetism and electricity were related, such as in stories of cutlery becoming magnetised, and
ship’s compasses suffering reverses in polarity, during thunder-storms.
What is more, many investigators were influenced by a philosophical argument which claimed to
show that the ‘forces of nature’ must have an underlying unity. Ørsted held this view, and seems to
have been searching on and off for years for magnetic effects due to a battery. It wasn’t at all
obvious, though, that the battery had to be in a closed circuit, in other words that there had to be a
current. When the effect was discovered (during one of Ørsted’s lectures, according to a popular
version of the story), it was not as anyone had guessed. Instead of pointing parallel to the wire, or
radially towards or away from the wire, the compass seemed to want to point at right angles to both
these directions.
[Note… Others had found compass needles being ‘affected’ during experiments with batteries. But
Ørsted was the first, as far as we know, to investigate systematically what was happening, and to
publish a clear, detailed description of the phenomenon.]
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5. Discoveries in Electromagnetism (Continued)
5.2 Ampère
Ørsted’s experiment was demonstrated at a meeting of the French Académie des Sciences. One of
those present was the mathematician André-Marie Ampère, a friend of Fresnel and a supporter of the
wave theory of light.
(http://www-history.mcs.st-and.ac.uk/history/Biographies/Ampere.html )
Ampère immediately plunged into an intense period of investigations. He reported discoveries at a
rate of around one a week for the next two or three months.
Improved version of Ørsted’s experiment
One of the first things Ampère did was to use magnets to cancel the effect of the Earth on the
compass magnet, over a region around the wire. He then found that even when it was not very close
to the wire, the compass magnet pointed at right angles to the wire and tangentially to circles around
the wire. [Ampère referred to electric current in the wire, and used this term consistently, with the
convention that the current in a wire is from the positive terminal of the battery to the negative.]
Forces between current-carrying wires
Ampère went on to demonstrate a totally new phenomenon: that wires carrying currents exert
forces on each other. Parallel wires attract each other if carrying currents in the same direction,
and repel if the currents are in opposite directions. On the left is Ampère’s diagram of his
apparatus. The parallel wires are AB (fixed to the base) and CD (able to swing on pivots E and
F).
Coils and Magnets
Ampère believed that the basic forces involved between his parallel wires, and between the wire and
the magnet in Ørsted’s experiment, were forces between currents.
So Ampère believed there were currents inside magnets? Yes. He strengthened his case by
showing that current-carrying coils and solenoids behaved very much like magnets...
• He showed that the ends of two coils seemed to attract and repel each other like the poles of
two magnets.
• He took the wires from the ends of a solenoid (AB in the right hand diagram) back through
the inside of the solenoid and out through the centre, then taking the wires up and down to
cups of mercury (N and M), connected to the terminals of a battery. Thus the solenoid could
turn freely. He found it to behave like a compass magnet.
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5. Discoveries in Electromagnetism (Continued)
5.2 Ampère (Continued)
Ampère’s Theory of Magnetism
What might be the paths of currents inside magnets to
make magnets behave like solenoids? At first Ampère
thought they might be big loops, like the turns of a coil.
He then took up a suggestion of Fresnel, that the loops
were ‘molecular’, in other words on a minute scale. In a
magnet the loops’ axes were supposed to be roughly
parallel (see diagram); in unmagnetised iron they were
supposed to be arranged randomly.
Current elements
Ampère regarded a series circuit as made up of a succession of ‘current elements’, that is very short,
near-enough-straight lengths of current-carrying conductor.
He wanted to find a formula for the force between two current elements which would do the same
for current elements as Coulomb’s inverse square law did for stationary point charges. But it needed
to be more complicated as it had to take account of the angles, (,  and ) between the current
elements, and between them and the line joining them. Take a quick look at the formula Ampère
decided upon, by courtesy of
www.rwgrayprojects.com/energy/VACE/calc/calc01.html (top four lines only)
To find the force that a whole circuit (1) exerts on circuit
2, you would need to add up all the forces that all the
current elements in 1 exert on all the elements in 2. This is
every bit as difficult as it sounds, except for certain
symmetrical cases, like long straight wires. Ampère had to
try various formulae for the force between current
elements until he found one which gave answers for forces
between circuits which agreed with experiment. [There are
other possible formulae which do so.]
Ampère was not the only one in France to be galvanised
into action by Ørsted’s discovery. Jean-Baptiste Biot and Félix Savart discovered that the torque on a
compass magnet due to a long straight current-carrying wire varied inversely with the distance of the
magnet from the wire. Like Ampère, they developed the idea of current-elements.
Self-test questions on Ørsted and Ampère
(1)
(2)
(3)
(4)
(5)
(6)
(7)
If you haven’t already done so, find out Ørsted’s nationality.
In Ørsted’s experiment the tendency of the magnet to point in directions tangential to circles
around the wire was probably the result least expected. Which two directions might have been
considered less strange?
How did Ampère’s ‘improved’ version of Ørsted’s experiment make it more conclusive?
(a) What is the basis of the definition of the SI unit of current?
(b) Discuss the appropriateness of naming it after Ampère.
Do physicists today believe that a magnet’s magnetism has anything to do with small-scale
electric currents inside it?
Explain why the force between current elements cannot be measured directly.
Find, in your list of formulae, the one which contains Biot’s and Savart’s discovery about the
long straight wire.
14
5. Discoveries in Electromagnetism (Continued)
5.3 Faraday
Michael Faraday is perhaps the best known and most
admired of nineteenth century scientists. His career
began with a fairy-tale ‘elevation’ from bookbinder’s
apprentice to Humphry Davy’s assistant at the Royal
Institution.
(www.rigb.org/rimain/heritage/faradaypage.jsp)
[The first three chapters of Michael Faraday and the
Royal Institution by J Meurig Thomas set the scene. The
whole book is very readable.]
Faraday was more an experimental scientist than a
theorist, but he had extraordinary, almost intuitive,
insight. He had the patience to tease out the details of
the effects he investigat-ed, and the flair to judge which
were important.
His achievements included the discovery of benzene, the
liquefaction of several gases, and the formulation of the
laws of electrolysis. He discovered that materials other
than iron experienced forces (even though weak or very
weak) when placed near the poles of a magnet.
It is his work in electromagnetism for which he is
probably most famous…
Faraday, like the French scientists, was
stimulated by Ørsted’s discov-ery. But,
unlike them, Faraday had no maths beyond
arithmetic, nor was he convinced that
mathematical theories, such as those using
‘curr-ent elements’, served much purpose.
Instead, Faraday’s ‘feeling’ for the wireand-magnet phenomenon, led him to
devise set-ups in which rotations took
place – see diagram. On the left hand side,
the uppermost pole of a magnet partially
immersed in mercury rotated about a
current-carrying wire. On the right hand
side a current-carrying wire rotated about
the uppermost pole of a magnet. The wire
was pivoted at its top end, and dipped into
mercury at its lower end. Check that you
can trace the path of the current.
In these experiments, as in those of Ørsted
and Ampère, electric currents produced magnetic effects. But magnets hadn’t been shown to produce
currents. Faraday’s instinct was that there must be such an effect, “magnetism causing electricity”; it
just needed to be found. Over the next ten years, he made several attempts to find it. Success came
on the twenty-ninth of August, 1831…
15
5. Discoveries in Electromagnetism (Continued)
5.3 Faraday (Continued)
The Discovery of Electromagnetic Induction
Faraday’s famous laboratory diary entry for August 29th 1831 (with a little more punctuation added)
begins as follows:
“Have had an iron ring made (soft iron); iron round and 7/8 inches thick and ring 6
inches in external diameter. Wound many coils of copper round, one half of the
coils being separated by twine and calico – there were 3 lengths of wire each about
24 feet long, and they could be connected as one length or used as separate lengths.
[…] Will call this side of the ring A. On the other side but separated by an interval
was wound wire in two pieces together amounting to about 60 feet in length, the
direction being as with the former coils. This side call B.
Charged a battery of 10 pr plates [10 pairs of plates] 4 inches square. Made the coil
[coils] on B side one coil, and connected its extremities by a copper wire passing to a
distance and just over a magnetic needle (3 feet from iron ring) then connected the
ends of one of the pieces on A side with battery; immediately a sensible effect on
needle. It oscillated and settled at last in original position. On breaking connection
of A side with battery, again a disturbance of the needle.”
Notes and self-test questions on the diary extract
• The coils were insulated from each other and from the ring.
• The two coils on side B were connected in series. [How does Faraday express this?]
• In this first experiment, Faraday used only one of the coils on side A; the other coils on side A
might as well not have been there.
• In the language of transformers, what are coils A and B?
• In magnetic terms, what does coil A do when connected to the battery?
• Faraday used Ørsted’s set-up, with wire and compass needle, as a ‘galvanometer’ to detect any
current in the coil B circuit – pick out the phrase Faraday uses to describe the arrangement. [In
fact his galvanometer wasn’t very sensitive, and he went on to use more sensitive instruments.]
• Why did Faraday place the galvanometer as far as 3 feet away from the ring?
• The current in the B circuit – Faraday soon started calling it the induced current – was only
transient; it was present only when the current in A was turned on and off.
This is probably the main reason why Faraday took so long to find ‘magnetism causing
electricity’. No-one seems to have guessed that the effect would take place only when a change
was occurring.
16
5. Discoveries in Electromagnetism (Continued)
5.3 Faraday (Continued)
Further Exploration of Electromagnetic Induction
Faraday knew he had made a major discovery, and set about a thorough investigation of the
phenomenon. He soon found, as he had expected, that even without iron, a changing current in one
circuit could induce currents in a nearby circuit, though the effect was much weaker than with iron
present.
If there were any doubts that the induced current was a magnetic effect, Faraday put paid to them by
thrusting one end of a bar-magnet into a solenoid connected to a galvanometer. The needle deflected
in one direction when the pole was thust in, returned to its zero position and stayed there if the
magnet was left stationary inside the solenoid, but deflected in the opposite direction when the pole
was withdrawn. (http://micro.magnet.fsu.edu/electromag/java/faraday2/ - not historical but fun)
Magnetic Lines of Force
Not only did Faraday demonstrate many instances
of electromagnetic induction, he developed a
simple but powerful way of visualising when it
would take place.
He relied on lines of force (now called lines of
flux). These are the curved lines that can be
‘plotted’ with iron filings or a compass magnet. In
Faraday’s diagram (of 1832) they arise from a
magnet, AB.
Faraday explains that if a conductor is part of a
closed circuit, a current will flow in it when it ‘cuts’ lines of force. In the diagram the conductor PN
which he draws is a knife blade – re-inforcing the cutting metaphor. He gives a rule for the direction
of current flow which is equivalent to the (later) Fleming’s Right Hand Generator Rule.
• In Faraday’s diagram A is the North pole of the magnet. If PN is moved upwards what will be the
direction of current flow through it (if the circuit is completed)?
This picture of cutting lines of force doesn’t really seem to apply to Faraday’s original experiment
with the ring of iron. There were no moving conductors (or magnets). But the notion of lines of force
can still be used… At the point of turning on the current in A the number of lines of force going
around inside the ring, and therefore ‘linked’ with coil B suddenly increases. The reverse happens
when the current in A is turned off.
The rule that a current is induced when there is a change in the number of lines of force linking a
circuit changes fits all cases of electromagnetic induction, including…
• plunging one pole of a magnet into a coil – draw the ‘before’ and ‘after’ pictures, including some
lines of the magnet’s lines of flux.
• part of a circuit cutting lines of force: the number of lines linked with the complete circuit will
change as a result of the change in area enclosed by the circuit.
17
5. Discoveries in Electromagnetism (Continued)
5.3 Faraday (Continued)
A Quantitative Law
Faraday came close to a quantitative rule when he wrote:
“If a wire moves across lines of force slowly, a feeble current is produced in it,
continuing for the time of the motion; if it moves across the same lines quickly, a
stronger current is produced for a shorter time.”
We nowadays sum up electromagnetic induction in the equation:
E

t
We see that Faraday’s insights have been ‘developed’ considerably…
• The equation deals with e.m.f. rather than current, since the induced e.m.f. does not depend on the
resistance of the circuit (whereas the current does).
•  represents Faraday’s idea of the number of lines of force linking a circuit. Check that you can
define  the modern way!
• The minus sign acknowledges the insight of Heinrich Lenz, working in St Petersburg in 1834.
Check you can state Lenz’s Law.
• The proportionality was deduced around 1845 by Franz Neumann (from Ampère’s work!). In S.I.
the proportionality constant is 1, so we can use ‘=’ rather than ‘’.
Action at a Distance?
How does a current-carrying wire influence a compass magnet, or exert a force on another currentcarrying wire, or, if the current is changing, induce a current in another circuit? How does the one
thing (call it ‘X’) influence the other, ‘Y’, even though there’s empty space in between X and Y?
In general, continental physicists (Ampère and others) saw this ‘action-at-a-distance’ as a thing that
simply happens, not requiring explanation. The work of the physicist, they thought, was to find
mathematical laws for the forces between X and Y.
Faraday, though, was not content with action-at-a-distance. Something had to be going on in the
space between X and Y in order to convey an influence from one to the other. Faraday felt that lines
of force were involved. He knew this was controversial.
[In most of his writings Faraday used the term ‘magnetic lines of force’ uncontrovers-ially to mean
lines (or curves) which tell you which way a compass magnet will point, or iron filings will line up,
if you put them in the vicinity of a wire or magnet.]
Electric Lines of force
Faraday also developed the idea of electric lines of force, starting on positive charges and ending on
negative charges. They can be plotted by using a non-conducting pivoted needle, with a positive
charge at one end and a negative at the other. Although they have some of the properties of magnetic
lines of force, the two sorts of line mustn’t be confused.
Some of the lines of force for a charged capacitor
are sketched in the diagram.
[Faraday found out a great deal about capacitors.
In particular he investigated dielectrics and their
effect
on
capacitance.]
18
6. Electromagnetic Waves
6.1 Faraday
Faraday drew a clear distinction between his experimental researches and his ‘speculations’ for
which there was little experimental evidence. He talked about one such speculation when he had to
fill in for a Royal Institution guest speaker who had taken fright and run away. Here are some
extracts from a summary Faraday wrote for a friend. Referring to electric, magnetic and gravitational
lines of force…
“[We can] affect these lines of force in a manner which may be conceived as partaking of the nature of a shake or lateral vibration. For suppose two bodies, A, B, distant
from each other and under mutual action, and therefore connected by lines of force,
and let us fix our attention upon one resultant of force having an invariable direction
as regards space; if one of the bodies move in the least degree right or left […] then
an effect equivalent to a lateral disturbance will take place in the resultant […]
My view which I am so bold as to put forth considers, therefore, radiation as a high
species of vibration in the lines of force which are known to connect particles and
also masses of matter together. It endeavours to dismiss the ether, but not the
vibrations. The kind of vibration which, I believe, can alone account for the wonderful, varied, and beautiful phenomena of polarization, is not the same as that which
occurs on the surface of disturbed water, or the waves of sound in gases and
liquids, for the vibrations in these cases are direct, to and from the centre of action,
whereas the former are lateral. It seems to me, that the resultant of two or more
lines of force is an apt condition for that action which may be considered as equivalent to a lateral vibration; whereas a uniform medium, like the ether, does not
appear apt, or more apt than air or water.
The occurrence of a change at one end of a line of force easily suggests a consequent
change at the other. The propagation of light, and therefore probably of all radiant
action, occupies time; and that a vibration of a line of force should account for the
phenomena of radiation it is necessary that such vibration should occupy time also.”
Notes and questions on Faraday’s Speculation
(1) What, in modern wave terminology, does he mean by a ‘shake, or lateral vibration?
(2) What, according to Faraday (first paragraph) would you have to do to send such a vibration
along a line of force? This is crudely illustrated for an electric line …
(3) Faraday says (second paragraph) that (for light) lateral vibrations are needed to account for
polarization effects.
(a) What phrase does he use to describe the vibrations in sound waves?
(b) What is the modern term?
(c) Is he right about the nature of surface water waves?
(4) Faraday’s speculations had implications for the luminiferous ether. [Revise section 4.4 – if
necessary!] These implications are summed up in one short sentence in the second paragraph.
Which sentence?
Faraday’s idea was indeed bold. It was nothing less than an attempt to link light and
electromagnetism. To be considered a successful attempt, it would need developing into a theory
which could make predictions, including quantitative ones.
19
6. Electromagnetic Waves (continued)
6.2 Maxwell
James Clerk Maxwell was arguably the greatest theoretical
physicist of the nineteenth century. Unlike Faraday, Maxwell
was born to well-to-do parents, and he received a first class
education, including a thorough training in mathematics.
Maxwell was brilliant at spotting analogies between different
branches of physics, developing them mathematically – and
knowing when to drop the analogy. His most far-reaching
work was in kinetic theory of gases, and in electromagnetism.
(The following link may not work, but the URL is fine: wwwhistory.mcs.st-and.ac.uk/history/Biographies/Maxwell.html)
On Physical Lines of Force
This is the title of a four-part paper of 1861-2 in which
Maxwell sets out to “examine magnetic phenomena from a mechanical point of view, and determine what
tensions in, or motions of, a medium are capable of producing the mechanical phenomena observed.”
• The ‘mechanical phenomena observed’ are the attractions and repulsions between poles of magnets.
He goes on to hint that his ‘medium’ theory will also account for electromagnetic effects such as
induced currents.
• Since magnets will ‘work’ in a vacuum, Maxwell’s medium must fill even ‘empty’ space. [An
invisible, space-filling medium was not a new idea – revise section 4.4].
Maxwell’s starting point was magnetic lines of force. He writes…
“[If] we strew iron filings on paper near a magnet, each filing will be magnetized by
induction, and the consecutive filings will unite by their opposite poles, so as to form
fibres, and these fibres will indicate the direction of the lines of force. The beautiful
illustration of the presence of magnetic force afforded by this experiment, naturally
tends to make us think of the lines of force as something real, and as indicating
something more than the mere resultant of two forces, whose seat of action is at a
distance and which do not exist there at all until a [compass magnet or iron filing] is
placed in that part of the field. We are dissatisfied with the explanation founded on the
hypothesis of attractive and repellent forces directed towards the magnetic poles […]
and we cannot help thinking that in every place where we find these lines of force, some
physical state or action must exist […]”
• What, then, was Maxwell’s take on action-at-a-distance? [See Section 5.3]
The properties Maxwell gave his space-filling medium allowed it to form into lines of force. The structure
of the medium was machine-like. He showed that the machinery seemed to account for the phenomena of
electromagnetism.
On the next three pages we look in some detail at Maxwell’s ‘machinery’. It may seem weird and quite
different from anything you’ve met in Physics before, but the basic ideas aren’t particularly difficult. If
you do find it a struggle, don’t give up: a general feel for what Maxwell was up to is worth having, even if
you
lose
some
of
the
details.
20
6. Electromagnetic Waves (continued)
6.2 Maxwell (continued)
Vortices
Maxwell asks us to suspend disbelief and to suppose that space is
filled with elastic beads. If a bead spins about an axis [diagram (a)],
it will become Smartie-shaped (like the Earth), contracting along its
axis and expanding sideways. He called the spinning beads ‘vortices’
– whirlpools.
Diagram (b) shows some of the lines of force between two opposite
magnetic poles attracting each other. It is as if the lines are under
tension, pulling the poles together, and are pushing out sideways,
pushing each other apart. This is just what would happen if the axes
of the spinning beads lie along the lines of force. So magnetic lines of
force are imagi-nary lines along which lie the axes of spin of the
vortices.
The angular velocity of the vortices was proportional to the field
strength. No field strength meant no spin.
Idlers
If you could look along any line of force going from the North pole
of one magnet to the South pole of another, the vortices would be
spinning in the same sense – anticlock-wise, let us suppose. This
presents a problem if space is chock-a-block with vortices. Between
a North and South pole, they are all rotating in the same sense, so
where vortices on adjacent lines of force touch, the vortex surfaces
will be moving in opposite directions, and will interfere with each
other’s motion [diagram (c)].
Maxwell’s solution was to suppose the vortices to be separated by ball-bearing-like ‘idlers’ [as in (d)]. By
rotating in the opposite direction to the vortices, the idlers enable the vortices to rotate in the same
direction as each other. Note: idlers never slip on vortices.
Maxwell’s (in)famous ‘honeycomb’ diagram of his ‘vortex medium’ is given below. Try not to worry
about the sharp corners and the 2-dimensionality; it is just a stylised way of showing space completely
filled with vortices separated by idlers. But, even so, could Maxwell seriously have believed that space
was full of ‘machinery’ of this sort? He wrote:
“The conception of a particle having its motion
connected with that of a vortex by perfect rolling
contact may appear somewhat awkward. I do not
bring it forward as a mode of connexion existing in
nature, or even as that which I would willingly assent
to as an electrical hypothesis. It is, however, a mode
of connexion which is mechanically con-ceivable, and
easily investigated, and it serves to bring out the
actual mechanical connexions between the known
electro-magnetic phenomena; so that I venture to say
that anyone who understands the provisional and
temporary character of this hypothesis, will find
himself rather helped than hindered by it in his search
after the true interpretation of the phenomena.”
Let us now see how it does help…
21
6. Electromagnetic Waves (continued)
6.2 Maxwell (continued)
Ørsted revisited
Spinning wasn’t the only motion Maxwell allowed his idlers. They
could also move ‘sideways’. The diagram shows a line, I, of idlers
moving (‘translating’) to the right without spinning. They must exert
tangential forces on the vortices with which they are in contact, making
them rotate as shown. This mot-ion spreads outwards from I via
spinning idlers and vortices.
In this 2-dimensional diagram, the vortices above I are being made to
spin anticlockwise, those below I, clockwise. So we are looking at a
section through lines of force going in circles around I. But we know
that an electric current in a straight wire has circular lines of force
around it. So a line of translating idlers must constitute an electric
current!
• Look again at Maxwell’s ‘honeycomb’ diagram – especially the
arrows – and spot the one (zigzag) line of translating idlers. [Note: in the fourth row down of
vortices, all four should be spinning clockwise!]
Self-induction
This material in this box will not be tested. It should, though, be of interest to anyone
who is also studying the Further Electromagnetism and A.C. Theory option.
The vortices have inertia and will acquire kinetic energy when made to spin. This
energy will have to come from the line of translating idlers that set them in motion,
in other words from the electric current. So the current will experience an opposing
e.m.f., when the current is increasing. Once it reaches a steady value, the line of
idlers will be translating at a constant speed, and the vortices spinning at a constant
angular velocity, so they will not be acquiring KE. If the current decreases, the
vortices will give back energy to the current, opposing its decrease, so there will be
an e.m.f. in the other sense.
This ‘explains’ the phenomenon of self-induction, which had been discovered
independently in the early 1830s by Joseph Henry in America and by Faraday.
•
Make sure you know the definition of e.m.f..
•
Revise, or look up, the defining equation for self-inductance, L, and think
about how it sums up the phenomenon of self-induction.
[We cannot, it should be said, calculate L for an isolated straight wire; we have to
take into account a ‘return path’ for the current (such a parallel wire).]
• You should now have some inkling of the capabilities of Maxwell’s ‘machinery’. In fact (with the
help of rather a lot of mathematics) Maxwell showed how it would give rise to all the known
effects of electromagnetism, including forces between currents and the e.m.f. induced in a
conductor cutting lines of force.
• But could the machinery tell us anything about electromagnetism that we didn’t already know? In
other words, could it be used to make predictions?
22
6. Electromagnetic Waves (continued)
6.2 Maxwell (continued)
Transverse Waves
We now look in more detail at how a current-carrying wire sets up a magnetic field around it.
Maxwell’s machinery predicts that when the current is switched on the field will take time to spread
out. The crude diagram below helps to explain this...
Suppose an idler, i, starts to turn. Because of its inertia, the vortex V ‘above’ i will not turn
immediately, and i will roll to the left. But i will exert a tangential force on V, giving an anticlockwise
torque on V, which will deform as shown, as it is made of elastically deformable material. Soon, the
whole of V will start to turn anticlockwise, the deformation and stress will disappear and i will return
to its original position. As it starts to turn, V will turn the idler ‘above’ it and the same thing will
happen all over again for the ‘next vortex out’, and so on.
Don’t worry if you struggled with the last paragraph. The points to grasp are these...
•
A magnetic field propagates outwards from its source at a finite speed.
•
The ‘wavefront’ of the spreading magnetic field is accompanied by temporary stress on the
vortex material. Maxwell interpreted this stress as an electric field. The vortices are
temporarily distorted and the idlers temporarily displaced. Maxwell called their motion a
‘displacement current'. The direction of the electric field is the direction of idler displacement.
•
The magnetic field and the electric field are at right angles to each other, and to the direction
of travel of the disturbance. Maxwell’s machinery is predicting transverse waves.
23
6. Electromagnetic Waves (continued)
6.2 Maxwell (continued)
Speed of travel of ‘Vortex’ waves
Maxwell derived a formula for the speed at which the transverse waves would travel, in terms of the
stiffness and the density of the vortex material. But for Maxwell’s ‘machinery’ to reproduce
electromagnetic effects properly, the stiffness and density had to be expressible in terms of constants
which appear in the equations of electromagnet-ism. The wave speed formula could then be written
(using modern notation) as
V 
1
0 0
0 is the permeability of free space, and 0 is the permittivity of free space. V is the speed of the waves
in so-called empty space, where there is nothing (except vortices and idlers!)
Maxwell evaluated the right hand side of this formula using electrical measurements which had
already been made (in Germany). He found:
V = 310 740 000 000 millimetres per second.
He also noted the speed of light, as measured fairly recently in France:
VL = 314 858 000 000 millimetres per second.
He then remarked, in one of the most famous sentences in the history of Physics:
“The velocity of transverse waves in our hypothetical medium, calculated from the
electro-magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with
the velocity of light calculated from the optical experiments of M. Fizeau, that we can
scarcely avoid the inference that light consists in the transverse undulations of the same
medium which is the cause of electric and magnetic phenomena.”
The Cheshire Cat
The equations relating to Maxwell’s ‘machinery’ could be expressed as relationships between
electromagnetic quantities. Most of them were versions of the known laws of electromagnetism, such
as Coulomb’s Law and Faraday’s Law of electromagnetic induction. One sub-set of the equations,
though, was entirely new. It contained the idea that a changing electric field had lines of magnetic
force curling around it.
Maxwell realised that the equations contained everything that his machinery had to say about
electromagnetism. He kept using the equations and stopped referring to the machinery. [Recalling
Alice’s Adventures in Wonderland, someone later commented that the Cheshire Cat had disappeared,
but its grin remained.] In fact Maxwell still believed that electromagnetic influences did travel by
means of a medium, but he stopped investigating the workings of any particular hypothetical medium.
The equations themselves are enough to predict transverse waves. The waves emitted from a charge
oscillating up and down can be represented as shown, at one instant.
An instant later the ‘profile’ of electric and magnetic fields will have moved to the right. Following the
spirit of Maxwell’s equations, we explain their propagation in this way.. The changing electric field
gives rise to a (changing) magnetic field [Maxwell’s discovery] and the changing magnetic field gives
a (changing) electric field [Faraday’s discovery], and the changing electric field gives a changing
magnetic field and so on. Maxwell was claiming that this was light!
24
6. Electromagnetic Waves (continued)
6.2 Maxwell (continued)
Self-test Questions
(1) Find out in which country was Maxwell born and brought up.
(2) What was Maxwell trying to do, when he invented his ‘medium’ of vortices and idlers?
(3) (a) What was different in Maxwell’s medium when there was a magnetic field?
(b) What, in terms of vortices, gave the direction of the field?
(c) And what gave the magnitude of the field strength?
(4) What, in terms of vortices and idlers, was an electric field?
(5) What two properties of the vortex medium determined the speed at which waves would
propagate?
(6) Explain the remark about the Cheshire cat. What does its grin represent?
(www.ruthannzaroff.com/wonderland/Cheshire-Cat.htm )
(7) (a) Was anything important lost when Maxwell ‘ditched’ the machinery of the vortex medium
and just kept the equations?
(b) Do equations explain things?
(c) What counts as an explanation in Science?
25
6. Electromagnetic Waves (continued)
6.3 Hertz
Maxwell’s work commanded great respect, but by no means everyone was convinced it was correct.
What in particular was needed was a direct experimental demonstration that electrical oscillations
could give rise to transverse waves. This, and more, was provided by Heinrich Hertz between 1887
and 1889.
Hertz was working with very high frequency electrical oscillations produced by the apparatus shown
in replica on www.sparkmuseum.com/HERTZ.HTM.
When a spark occurred between the small spheres the air in the gap between them had ‘broken down’
and become a conductor. There was a current in the air gap and the rods either side. This current
dropped to zero, reversed in direction, rose to a maximum, fell to zero, reversed and so on. The
frequency of these electrical oscillations was determined by the system’s inductance (mainly due to
the rods) and its capacitance (mainly due to the large spheres). Hertz estimated the frequency to be 10 8
cycles per second.
When the sparking occurred, Hertz could also see sparks jumping across a narrow gap in a wire ring,
even when the ring was a few metres away. Further investigation strongly suggested that transverse
waves were involved.
Hertz modified his apparatus to improve its range and precision. The ‘transmitter’ lost its large
spheres, and the oscillation frequency increased by about 10 times. Hertz found that the ‘radiation’
could be concentrated into a beam using a concave metal reflector. [See diagram (size of rods and
spheres exaggerated).] To detect the radiation he started using a pair of straight wires with an offset
spark gap. The gap could be adjusted with a micrometer screw. The longer the sparks he could get, the
stronger the electric field.
Stationary Waves
Hertz placed a large flat metal sheet in front of the transmitter and facing it. He moved the detector
between the transmitter and the sheet and reported very distinct maxima and minima. He could
distinguish nodal points at the wall and at 33, 65 and 98 cm distance from it. He concluded that
interference was taking place, leading to a standing wave pattern. Here was clear wave-like behaviour.
•
Which two ‘streams’ of waves were interfering?
•
What wavelength was Hertz using?
•
What was the frequency of the oscillations?
•
Which devices in the 21st century use this sort of frequency? ‘v.h.f.’ radios, televisions with
traditional (spiky) aerials, or microwave ovens?
26
6. Electromagnetic Waves (continued)
6.3 Hertz (continued)
Polarisation
No sparking occurred in the detector when it was turned
so its wires were horizontal, as shown. Hertz deduced that
the waves were polarised, with the electric field direction
parallel to the rods in the transmitter (as predicted by
Maxwell’s equations). Clearly they were transverse
waves.
With the detector wires vertical again, Hertz interposed a
grille of parallel wires between the transmitter and
detector. The detector sparking was unaffected when the
wires were horizontal, but no sparks could be had when
the grille was turned so that the wires were vertical.
•
What special material, containing parallel
molecules, can do for light what Hertz’s grille of
wires did for u.h.f. waves?
Refraction
Hertz’s account (translated by D E Jones) began
“In order to find out whether any refraction of the ray takes place in passing from air to another
insulating medium, I had a large prism made of so-called hard pitch, a material like asphalt. The base
was an isosceles triangle 1.2 metres in the side, and with a refracting angle of nearly 30°. The
refracting edge was placed vertical, and the height of the whole prism was 1.5 metres. But since the
prism weighed about 12 cwt [600 kg or 0.6 tonne], and would have been too heavy to move as a
whole, it was built up of three pieces, each 0.5 metres high, placed one above the other.”
What Hertz found is summarised in the plan above. Observe that he was now using a concave reflector
behind his detecting wires as well as behind the transmitting rods.
• Hertz calculated the refractive index of the pitch as 1.69. Check this figure, by drawing relevant
normals and calculating angles. Note the symmetry.
Consequences
Hertz’s findings were soon accepted as establishing the reality of electromagnetic waves. The
possibility of using the waves for communication was taken up by several people, most famously by
Guglielmo Marconi. On 12th December 1901, he reported that signals sent from Cornwall had been
received in Newfoundland. And now we have radio, television and mobile phone technology, all based
on
electromagnetic
waves.
27
7. Assault on the Ether
7.1 The Triumph of the Ether?
If light is a wave, surely it has to have a medium to travel in? This was the compelling reason for
belief in the existence of a ‘luminiferous ether’ from about 1820 onwards. [Revise section 4.4] In the
1860’s Maxwell showed that a medium with the right structure might be able to account for
electromagnetic effects – of which light was one. Hertz’s work in the late 1880s seemed to confirm
Maxwell’s ideas. At least in Britain, few physicists doubted the existence of the ether, though its
structure was … debatable.
There was no direct evidence for the ether’s existence. But Maxwell realised that in principle such
evidence was available… Since the time of Galileo people had stopped believing that the Earth was
the stationary centre of the universe, so it would be odd to think of the ether as stationary relative to
the Earth. Stationary relative to the Sun seemed a much better bet. So as the Earth moves round the
Sun it is presumably also moving through the ether, and the motion is in principle detectable.
• The Earth’s orbit is roughly a circle of radius 1.5  1011m. Show that the Earth’s orbital speed is
3.0  104 m s1. What is this as a fraction of the speed of light?
7.2 The Michelson Morley Experiment (1887)
The challenge of detecting the motion of the Earth through the ether was taken up in America by
Albert Michelson.
(http://nobelprize.org/nobel_prizes/physics/laureates/1907/michelson-bio.html )
Michelson designed a piece of apparatus which came to be called an interferometer. The semi-silvered
plate acted as a beam-splitter, so light travelled from source to telescope by two routes: SOAOT and
SOBOT. Interference occurred between the light taking the different routes.
Suppose that the apparatus happened to be orientated so that the interferometer was moving to the left
through the ether. This is equivalent to the ether moving to the right past the apparatus, at velocity v,
say. [Think of a plane in a wind-tunnel.] As a result the observed interference pattern was expected to
change if the apparatus was turned about a vertical axis (see next page).
After an inconclusive first experiment, Michelson, joined by E.W. Morley (who had been making
precision measurements in a quite different area of science), redesigned the apparatus. It was now
mounted on a massive concrete block, floating in mercury, so it could be turned smoothly and was not
affected too badly by vibrations. By using multiple reflections, the effective length, L, of each arm,
OA and OB, was made to be 11 m.
28
7. Assault on the Ether
7.2 The Michelson Morley Experiment (Continued)
Light taking the route OAO
‘Ordinary’ waves, such as sound waves, travel at a fixed speed relative to their medium, so it was
assumed that light would travel at a fixed speed, c, relative to the ether. If the ether is itself rushing
past the apparatus at velocity v then the light should travel ‘downstream’ (OA) at velocity (c + v) and
‘upstream’ (AO) at velocity (c – v) relative to the apparatus (vector addition). The total time for the
light to travel OAO is therefore
L
L

c v c v
If there were no ‘ether wind’ the total time for AOA would be
2L
c
So the extra time taken to travel AOA because of the ether wind’ is
L
L
2L
tOAO 


cv cv c
8
1
Putting L = 11 m, c = 3.00000  10 m s , and v = 3.0  104 m s1 [Why?] gives
tOAO  7.3  1016 s
• You should check this. Try also using a better figure for c, e.g. c= 2.99792  108 m s1.
Light taking the route OBO
In this case the ether wind is at right angles to the ‘forward’ and ‘back’ paths OB and BO. According
to vector addition the velocity of light relative to the apparatus is reduced. However the delay due to
the ether wind turns out to be only half as much as for OAO.
In other words
tOBO  3.6(5)  10 16 s
So light will return to O, and from there to the telescope, in a shorter time via B than via A. The
difference in times is (tOAO – tOBO) which is 3.7  10-16 s.
Michelson and Morley took the wavelength of the light as 5.5  10-7 m, corresponding to a frequency
of 5.5  1014 cycles per second (5.5  1014 Hz).
Number of cycles occurring in 3.7  1016 s = 5.5 1014 Hz  3.7  1016 s = 0.20 cycles
Expected results and actual results
The light travelling via A is therefore delayed by 0.2 cycles compared with that via B. Suppose that
the apparatus is turned through 90°. The route OBO will now be the slower one, so the change in
delay will be 0.2 cycles – (–0.2 cycles) = 0.4 cycles. If, in the original orientation, A had been moved a
minute amount towards O so as to give full constructive interference between the light travelling the
two routes, then on turning the apparatus through 90° there would be almost complete destructive
interference.
In fact, Michelson and Morley had the apparatus adjusted so that A and B were not quite at right
angles to each other. This meant that the telescope revealed a pattern of parallel bright and dark fringes
much like Young’s fringes. When the apparatus was rotated through 90°, a 0.4 cycle change in delay
would make the fringe pattern shift by 0.4 of a fringe, so a bright fringe would almost be replaced by a
dark one and vice versa.
In fact hardly any fringe shift was observed. But OA might not have been parallel to the ether wind in
the first place, so Michelson and Morley kept the apparatus slowly turning, and examined the fringe
pattern at 16 orientations of the apparatus. They repeated the observations at different times of day and
night and at different times of year. The maximum shift they found was about 0.01 of a fringe. This
was, to all intents and purposes, negligible.
29
7. Assault on the Ether
7.3 After Michelson Morley
What do scientists do when a successful theory is contradicted by experimental evidence? Give up the
theory? This is not usually the first response. It certainly wasn’t when the Michelson Morley
experiment gave a null result. Rather than give up the idea of the ether, physicists tried to think up
explanations for why the ether did not show up in the experiment. Here are the two most famous…
• The ether in the neighbourhood of the Earth is dragged along by the Earth, rather as a moving ship
is surrounded with a layer of stationary water. So even though the Earth is moving around the Sun,
and even if the whole solar system is moving through the ether, there will be no ether wind on the
Earth’s surface.
The trouble with this idea was there were other effects which the ether theory could explain, but
only if the ether moved freely past the earth! [For interest only: the main such effect was ‘stellar
aberration’, which is explained in Banesh Hoffmann’s book, Relativity and its Roots – even though
‘aberration’ is not in the index.]
• As well as the ether wind changing the velocity of light relative to the interferometer, it also
changes the shape of the interferometer in a way which exactly neutralises the extra delay on the
upstream-downstream arm due to the velocity changes. This idea was put forward in 1889 by
George Fitzgerald, who was working in Dublin.
A similar explanation was offered independently by the Dutch physicist Hendrik Lorentz some
three years later. He claimed that the only change in shape was a contraction of the ‘upstreamdownstream’ arm. Using Maxwell’s equations, and making various assumptions about electrons
and the role of electromagnetic forces in holding matter together, he argued that all objects should
contract in the direction parallel to the ether wind.
7.4 Einstein
(http://www-groups.dcs.stand.ac.uk/~history/Biographies/Einstein.html)
Albert Einstein was barely known to the world of Science
until, in 1905, at the age of 26, three major papers by him
were published in the prestigious German scientific
journal Annalen der Physik. They have been described as
setting the agenda for Physics for the next hundred years.
The first paper contained the curious notion that light
might sometimes behave as if it consisted of packets of
energy, and the prediction of the photo-electric equation.
The second showed how to demonstrate the existence of
molecules by observations on Brownian motion.
The third paper was called (in translation) On the
Electrodynamics of Moving Bodies. It lays the
foundations of what is now called the Special Theory of
Relativity.
The theory takes two innocent-looking starting points, or ‘postulates’ and builds on them in a
ruthlessly logical fashion, to come to some momentous conclusions. The first postulate is the Principle
of Relativity…
7. Assault on the Ether
7.4 Einstein (Continued)
The Principle of Relativity
The laws of Physics are the same in all inertial frames of reference. All such frames are equivalent.
30
The Principle generalises the finding that mechanics experiments give exactly the same readings
when performed in a laboratory on a smoothly moving, non-accelerating train or aircraft as they do in
a ‘stationary’ laboratory. The train and the plane are (approximately) ‘inertial’ frames of reference –
ones in which a body at rest stays at rest, provided no resultant force acts on it. Inertial frames are the
only ones we use in A-Level Physics.
The generalisation that Einstein makes is that all laws of Physics, including those of electromagnetism
and light, hold good in all inertial frames. There is no privileged ether frame of reference, and in all
inertial frames of reference light travels through empty space at speed c given by
1
c
 0 0
But suppose the light source is moving towards the observer (in a laboratory equipped with rulers and
light-activated clocks accurate to the picosecond!). This is the same thing as saying that the observer is
moving towards the light source. Will the observer then measure a larger speed for the light? Not
according to Einstein…
Second Postulate
The speed of light is independent of the motion of its source.
• The Michelson Morley experiment was repeated in the 1920s using starlight and sunlight, rather
than a lamp in the laboratory. What was the point of doing these further experiments? [Again, no
directional differences were observed.]
The time of an event
To deduce things from the postulates we have to be very precise about what we mean by the time
when an event takes place. Einstein wrote [translated from the German]…
We have to take into account that all our judgements in which time plays a part are always judgements
of simultaneous events. If, for instance, I say, “That train arrives here at 7 o’ clock.”, I mean
something like this: “The pointing of the small hand on my watch to 7 and the arrival of the train are
simultaneous events.”.
It might appear possible to overcome all the difficulties attending the definition of ‘time’ by
substituting ‘the position of the small hand of my watch’ for ‘time’. And in fact such a definition is
satisfactory when we are concerned with defining a time exclusively for the place where the watch is
located, but it is no longer satisfactory when we have to connect in time a series of events occurring in
different places.
The way to deal with the problem is to have a clock at every place where an event might happen – and
to make sure the clocks are synchronised. We can in principle put a whole line of clocks down the
laboratory (or, if needed, a three-dimensional array of clocks).
Suppose we have a line of clocks at intervals of 0.30 m… How do we synchronise them? Before
starting them we could adjust their displays to read 0.0, 1.0 ns, 2.0 ns and so on as we go from left to
right along the line. We then trigger them to start by a light signal originating at the left hand end of
the line and travelling down the line past each clock.
•
How does this work? How long does it take the light signal to travel 0.30 m?
31
7. Assault on the Ether
7.4 Einstein (Continued)
A though-experiment
We shall look at the consequences of Einstein’s postulates in one
specific case, where we can imagine an experimental set-up and work
out what – according to the postulates – must happen. In other words we
shall do a thought-experiment (or Gedankenexperiment). [The term is
believed to have been invented by Ørsted!]
Suppose a light flashes close to the end, A, of a rod of length L. The
flash triggers a nearby clock to start. The light reflects off a mirror at the
other end, B, of the rod. When it has returned to A it triggers the clock to
stop. If the clock records a time interval  between the events of the
light leaving A and returning to A, then:…
2L = c .
Now suppose that the rod is actually moving through a laboratory at
speed v at right angles to itself. [This won’t affect the previous equation,
since this was written for the rod’s own frame of reference.]
In the laboratory frame of reference the light travels the path PQR (see
diagram below).
Clearly in the laboratory frame the light has had to travel further between its leaving the end A of the
ruler and its arriving back there. But the speed of light is the same in all frames. So the time, t,
between the light leaving A and the light returning to A must be greater than the time, , between the
same two events as measured in the rod’s frame of reference. This effect is called time dilation. Time
intervals are different for different observers!
32
7. Assault on the Ether
7.4 Einstein (Continued)
A thought experiment (continued)
How different are the time intervals measured in the two frames? It is easy to find out…
In the laboratory frame the rod moves a distance v t in the time t. But the light has travelled distance
c t.
So, applying Pythagoras’s theorem to either of the two right angled triangles in the diagram…
L2   12 ct    12 vt 
Substituting for L from the rod frame equation,
2

2
c    12 ct    12 vt 
Doing the squarings and multiplying through by 4,
1
2
2
2
2

c 2     c 2  t   v 2  t  that is c2     c2  v2
2
2
2
2
  t 
2

Dividing both sides by c2 and then taking the square roots of each side,     1  vc2
2
2
  t 
2
so
  1  vc2 t
2
Finally, dividing both sides by the square root,
t 

1  vc2
2
• Try to calculate t if  = 1.000000000 s and v = 1000 ms-1. Check that your calculator gives t
= 1.000000000 s. Time dilation doesn’t show up, even to 10 significant figures, for a relative
velocity of three times the speed of sound between the frames of reference. No wonder it is such an
unfamiliar idea!
• But for relative velocities approaching the speed of light the effect is large. Calculate  if  =
1.00 s and v = 3/5 c.
• The formula doesn’t just apply to this set-up, or just to flashes of light. The time interval between
any two events is greater in a frame of reference in which the events occur in different places than
in the frame in which they occur at the same place. The time interval in this latter frame is called
the proper time interval, .
• The effect has been confirmed by experiment and the formula checked.
(www.youtube.com/watch?v=gdRmCqylsME : a bit incoherent, but gives the idea.)
What causes time dilation?
Are measurements made in the rod’s frame of reference invalid because it is moving? No, all inertial
frames of reference are equivalent; none is favoured. In any case, an experimenter on the rod is
perfectly entitled to say that it is the laboratory which is moving!
Has the electronics of the rod’s clock been affected by its motion? No; the laws of Physics are the
same in all inertial frames. Nothing is different about the way the clocks run in the two frames.
Anyway, in the rod’s frame it is the laboratory clocks that are moving.
So what does cause time dilation? It is the non-independence of space and time, as acknowledged in
the term, space-time. The time interval between two events is least when measured in a frame of
reference in which the events occur at the same place. It is greater in a frame of reference in which the
events occur in different places, and there-fore have to have their times recorded by different clocks.
[Note the line of synchronised clocks shown in the laboratory frame diagram.]
[In fact what stays the same for two events if we go from one inertial frame to another is the quantity
c2 ()2 = {c2(t)2 – (x)2– (y)2– (z)2}. This looks a bit like Pythagoras’s theorem in 4 dimensions,
which is why time is sometimes called the fourth dimension.]
33
7. Assault on the Ether
7.4 Einstein (Continued)
Special Relativity results: not for learning
The time dilation thought-experiment was, as promised in the introduction, a small taste of Special
Relativity theory – but no more than a taste. Many other results, some of them equally extraordinary,
can also be deduced from the two postulates. The results include…
• Events which are simultaneous at different places in one frame of reference are generally not
simultaneous in other frames (moving with respect to the first).
• A ruler stationary in one frame of reference is shorter in any other frame moving parallel to the
ruler.
This might remind the alert reader of the idea of Fitzgerald and Lorentz (section 7.3) that the
upstream-downstream arm in the Michelson Morley experiment was shortened by its motion
through the ether. In fact some of Lorentz’s mathematics was very similar to Einstein’s – and
published before 1905, but his interpretation of the equations was very different. For example,
Lorentz argued that the ruler would be contracted in length compared with its length if stationary in
the ether frame of reference. According to Relativity theory there is no such special frame.
• Lengths at right angles to the relative velocity between frames of reference are the same measured
in either frame. We have already assumed this. Where?
• No object can move faster than the speed of light – in any frame.
• Some of the formulae of Newtonian mechanics have to be altered. The alterations usually only
make any significant difference for bodies moving very fast indeed (say above 1.0  106 m s-1).
• Mass and energy are equivalent. The conversion factor between units is c2.
• Maxwell’s equations are valid in all frames of reference, not just in one special ether frame, as
Maxwell and Hertz believed.
• The strengths of components of magnetic and electric fields vary according to reference frame. We
illustrate this with a thought-experiment…
If you want to learn more, Relativity and its Roots by Banesh Hoffmann is helpful.
Should you want to do some serious study, consider an internet search for a secondhand copy of An
Introduction to Special Relativity by James H Smith. It’s an old book (first published 1965) but it’s
down to earth and the explanations are very clear.
34
7. Assault on the Ether
7.5 Einstein (Continued)
Electrons moving side-by-side: a thought-experiment
Suppose two electrons emerge simultaneously with the same high velocity from electron guns side by
side. The electrons will repel each other so their paths will diverge.
Consider the ‘top’ electron. Home in on two events: (a) the electron leaves the gun, and
(b) the
electron hits a target, having been
repulsive force. In the laboratory frame (left hand diagram) these events are spatially far apart, and the
Now imagine we could ride along with the electrons, keeping pace with their horizontal motion (and
clutching a clock!). In this new frame of reference (the ‘electrons’ frame’), events (a) and (b) are only
slightly separated in space (by distance y). The time interval between the events is to all intents and
purposes the proper time, .
Since t is greater than  we must conclude that the repulsive force between the electrons is less in
the laboratory frame than in the electrons’ frame. The force reduction will be very small unless the
electrons’ speed approaches the speed of light.
Is this some weird new phenomenon? No – we can predict it from A-Level Physics, by a quite
different line of reasoning…
We first note that in the electron’s frame, the only force between the electrons is the repulsive
Coulomb force or electrostatic force. [Gravitational forces are negligible.]
In the laboratory frame the repulsive Coulomb force acts, but there is also an attractive force, because
moving charges constitute electric currents, and like currents attract. We could call this the Ampère
force. [See section 5.2.] We could also call it the magnetic force, because each electron sets up a
magnetic field and the other electron moves through this field and experiences a Motor Effect (BIl)
force.
This Ampère force is much smaller than the Coulomb force unless the electrons’ speed is approaching
that of light. All the same, the resultant force between the moving electrons will be slightly less than
that between stationary electrons.
But we arrived at this conclusion by a time dilation argument, without any appeal to Ampère forces:
that is to magnetic forces. It looks as if the only fundamental force between charges is the Coulomb
force, and magnetic forces are an effect due to measuring the force between charges in certain
reference frames. Quite an insight!
[To tell the whole truth, electric fields strengths also, generally, change according to the frame of
reference. In the thought-experiment, the repulsive Coulomb force between the electrons is actually
slightly increased when they are moving relative to us. But the attractive Ampère force is a greater
effect. If we take account of both effects the reduction in repulsive force turns out to be exactly as
calculated
from
the
time
dilation
argument.]
35
7. Assault on the Ether
7.6 Einstein (Continued)
Relativity and the Ether
Clearly, if all inertial frames of reference are equivalent and the speed of light (in empty space) is the
same in all frames, then the Michelson-Morley experiment would have had to give a null result: there
being no difference in the speed of light to detect!
• It would, though, be misleading to say that the Special Theory of Relativity explains the null result
of the experiment. Why?
Einstein was motivated at least as much by wanting to tidy up the theory of electro-magnetism as by
the null result of the Michelson-Morley experiment. In particular he did not like the idea of equations
which were valid only in a special frame of reference.
The Special Theory of Relativity held together well and made predictions which were confirmed in
the years that followed. The theory made no use of the idea of an ether, and took as a starting point the
non-existence of a special ether frame of reference. Physicists came to see the ether as being of no use
in explaining anything. They stopped believing in it.
• Why, in the first place, did the ether become such an important part of nineteenth century thinking
on light? What role was it supposed to play?
• What major discovery arose from using an ether theory of electromagnetic fields?
Some quick Revision
(1) Name the two scientists who did most to establish the wave theory of light between 1800 and
1820.
(2) Name three scientists who made discoveries in electromagnetism between 1820 and 1840, and
make summaries of what they discovered.
(3) Whose concept in (electro)magnetism did James Clerk Maxwell build upon when he started to
develop his idea of a vortex medium? What was the concept?
(4) What was the inference from the calculated value of
1
 0 0
which, according to Maxwell, ‘we
can scarcely avoid’?
(5) What were Einstein’s two postulates on which he based the Special Theory of Relativity?
(6) What is meant by time dilation?
What happened next?
In the 21st century we still believe that light travels like a wave, with oscillating electric and magnetic
fields, and that it doesn’t need a medium.
When it comes to understanding how light interacts with matter we need to think of light as photons.
The most highly developed theory we have in Physics is called Quantum Electrodynamics (QED). It
explains electromagnetic forces in terms of the exchange of photons.
If you’re remotely interested, read: QED: The Strange Story of Light and Matter by Richard
Feynman. He was one of the inventors of the theory, a colourful character, a brilliant teacher and
writer – and one of the greatest physicists of the twentieth century.
36
GCE Physics – Teacher Guidance
4 December 2007