Rosetta Stone - Mike Fuller
Appendix 1: Magnetism, Magnetic fields and Electromagnetism – some basics.
Historical origins - forces of attraction and repulsion between magnets, and the alignment
of magnets in magnetic fields.
Introduction
Magnetism was discovered before recorded history, and so we must content
ourselves with apocryphal stories of its discovery, such as that of the Greek shepherd in
Magnetes, whose boots, or staff, we are told, stuck to the rocks on which he walked.
This was a manifestation of the force of attraction between magnets - one of the two
fundamental aspects of the behavior of magnets. The effect was known in Western
civilization from at least the 7th century BC, during the so called dark ages after the
collapse of the Mycenaean civilization and before the main flowering of the Greeks.
The second fundamental aspect of the behavior of magnets - the alignment of
magnets in magnetic fields, which led to the compass - was discovered much later. There
are references to magnetism in Chinese literature and mythology, and a version of a
compass was in use in China about 1000 years before the first direct reference to the
compass in Western literature (1086AD). The Chinese also believed in magnetically
favorable citing and orientation of buildings.
Magnetic fields
Why do magnets exhibit two such different types of behavior - why in some cases
do they experience a force of attraction, or repulsion, while in other cases they rotate in
place, like a compass needle? To explain this, we follow the usual approach of thinking
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about the behavior of magnets in terms of north and south poles. Just as there is a force
of gravitational attraction between any two masses, so there are forces between magnetic
poles. The magnetic force between two magnets is evidently much stronger than the
Newtonian gravitational force of attraction between their masses. The former is readily
apparent in everyday life, while a very delicate measurement is needed to observe the
gravitational attraction between two masses in the laboratory. The magnetic force is also
different from the gravitational force in that it is not always a force of attraction. There
are north (+) and south (-) poles and the force between like poles repels, while unlike
poles attract.
Let's start with gravity, which gives a force of attraction between all masses. In
describing the effects of gravity, the concept of a field is used. The word “field” is often
used without a lot of clarification, but the idea is very simple. For example, when you
watch the weather station on the TV, you will often see a map of temperatures for your
local area. This tells you what the temperature is at the depicted spot on the map. This
map is then a crude temperature field for the region. Here, we are not much concerned
with temperature fields, but the idea of a field is very general. Magnets generate magnetic
fields and magnets experience forces in magnetic fields. Electric charges experience forces
in electric fields. The field value tells us the strength and direction in which the magnetic,
or electrical force acts. Unlike these fields, which affect only magnets and electric charges,
all masses experience forces in the gravitational field. These then are the force fields we
met in everyday life.
Around a spherical mass, we can visualize a gravitational field, which is
everywhere pointed to the center of the sphere. It was Newton’s genius to see that just as
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the apple experiences this force and hence an acceleration toward the center of the earth,
so too does the moon. However, despite experiencing the acceleration towards the center
of the earth, the tangential velocity of the moon keeps it in its orbit about the earth. The
lines illustrating the direction of the gravitational force point to the center of the sphere.
The gravitational force is a maximum in this direction and is zero perpendicular to it. The
gravitational force at each point has direction and magnitude. We call such a quantity a
vector in contrast to a scalar quantity, such as temperature, which can be described by a
single number giving its magnitude. No direction is associated with the idea of
temperature, we simply describe how hot or cold something, or somewhere is. Returning
to our picture of the gravity field of a sphere, note that the lines must become closer
together as the sphere is approached. The increase in density of the lines is in proportion
to the increase in field strength and so the picture represents both the direction and
magnitude of the gravitational force.
A magnetic field is more complicated than a gravity field because there are
magnetic forces of attraction and repulsion between magnetic poles. Nevertheless, the
strength and direction of magnetic field vector can be indicated by magnetic lines of force,
which are analogous to the force lines of the gravitational field. They were introduced by
Michael Faraday in the first half of the19th century.
By convention, magnetic lines of force are drawn from north (+) to south (-)
poles. The number of lines of force per unit area is a measure of the strength of the field,
just as we saw in the gravitational case. Magnetic lines of force also have two other
properties.
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(1) They are under tension, which in the absence of other forces would cause them
to contract into a straight line between their anchored end points at the poles.
(2) They also have the property of mutual repulsion, which would in the absence
of other effects make the field lines balloon out away from their anchored ends.
Together these two properties govern the configuration of the lines of force of magnetic
fields. For example, they determine the familiar pattern of the lines of force around a bar
magnet, which can be seen by placing iron filings on a piece of paper immediately above a
magnet. As we describe, the geomagnetic field and other magnetic fields, we will
frequently make use of Michael Faraday's idea.
Forces of attraction and repulsion between magnets - magnets in inhomogeneous
magnetic fields.
We are now ready to explain the effects of magnetic fields on magnets, and so to
answer our question, why sometimes magnets are accelerated by some magnetic fields,
but on other occasions they rotate in place. If a small test magnet is brought close to a
larger magnet, as illustrated in figure 2.5, then the field at the end of the test magnet
closest to the big magnet will naturally be stronger than at the other. It will therefore
experience a greater force of attraction, than the force of repulsion of the pole at the other
end of the magnet. The test magnet will therefore experience a net force, and it will
accelerate towards the larger magnet. This acceleration can be spectacular - one does not
want to get between a magnet and the pole of a large magnet. If we reverse the test
magnet in our example, it will experience a force of repulsion and will be accelerated away
from the large magnet.
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The difference between the magnitude of the attractive and repulsive forces
experienced by the two poles of a magnet and the resulting net force on the magnet are the
basis of the forces of attraction and repulsion between magnets. They are the explanation
of innumerable applications of magnetism, from toys to the giant magnetic separators
used in the mining industry. The requirement is that the field varies significantly over the
length of the magnet - the magnetic field must be inhomogeneous for these effects.
Alignment of Magnets in homogeneous magnetic fields - the compass.
In a magnetic field, which does not vary significantly over the length of the magnet
- a homogenous field - the behavior of the magnet is quite different.
Both poles
experience equal and opposite forces, so no net force is experienced and the magnet stays
put. We can use a mathematical trick to analyze the forces on the two poles of the
magnet without worrying about its justification. We resolve the forces on the poles into
two components of force - one parallel and one perpendicular to the length of the magnet
as illustrated. We then see that there are equal and opposite components along the length
of the magnet. These have no important effect because the test magnet is too strong to be
pulled apart. However, the components perpendicular to the axis of the magnet are both
acting in concert, so that the magnet rotates to become parallel to the field lines. If the
magnet is free to rotate, it will align with the field, as a compass does. It is the universal
property of magnetic fields that magnets are aligned by them.
Conclusion.
As we saw from figure 1.4, the magnetic field of a bar magnet has a particularly
simple form, which we will frequently encounter in this book. For example, the magnetic
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field of the earth is to a good approximation equivalent to the field of a giant bar magnet at
the center of the earth.
As long as we do not get too close to a bar magnet, the field decreases with
distance from the center of the source magnet in a simple way, similar to, but faster than
the way the gravity field falls off with distance from a mass. The gravitational field falls
off with the square of the distance, so that if we move two units a way, the field falls to
one quarter. This is an inverse square law - the field decreases as the square of the
distance. However the magnetic field of the bar magnet falls to one eighth at the same
distance - an inverse cube law.
To summarize - within a magnetic field a magnet will be aligned if the field is
homogeneous, but in an inhomogeneous field it will also experience a force of attraction,
or repulsion, which will accelerate it. In developing these ideas about magnets we have
used the concept of magnetic poles and developed an analogy with the behavior of point
mass sources, which can also be extended to the idea of an electric field and the force
between electric charges.
Electromagnetism - the magnetic fields of electric currents, and the electric currents
induced by magnetic fields.
Introduction.
At this point a confession is in order. Although the concept of magnetic poles is a
convenient way of thinking about the behavior of magnets and magnetic fields, there is not
a scrap of evidence that magnetic poles exist. However, before the reader gives up on this
“book”, it is as well to realize that in much scientific explanation, we use images whose
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reality is to varying degrees questionable. For example, it is helpful to think of an
electron as a compact mass in orbit about the nucleus of the atom and we shall do so, but
a quantum mechanical view of the electron would be quite different and a better view. In
this same spirit, we shall use the convenience of magnetic poles, as did Gauss and other
giants in the field, but we will also follow a more satisfying explanation which will serve
us better throughout the rest of our story.
This better view of magnetism arises from the recognition of the relation between
electricity and magnetism. In the 17th century, Newton had seen that the falling apple in
the orchard and the moon in its orbit were controlled by the same gravitational force. He
had achieved a synthesis in the sense that he had explained phenomena seen on the earth's
surface and in the heavens by the same mechanism - gravity. In the 19th century, the
genius of Maxwell saw that magnetism and electricity could be related and he achieved
one of the greatest intellectual feats of all time in providing a synthesis of understanding
of the phenomena of electricity and magnetism culminating in Maxwell's equations. With
this synthesis, much of what we now call classical physics was understood. This led to
various unwise statements around the turn of the C19th to the effect that physics was all
over, and that all that remained was to dot a few i's and cross a few t's. However, we
digress too much.
To gain a better view of magnetism, we must understand the
phenomena, which led to Maxwell’s synthesis.
Electric currents and magnetic fields.
The origin of magnetism can be understood as a consequence of the motion of
electric charges - an electric current. Whenever an electric current flows negative electric
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charge in the form of electrons, or positively charged ions are in motion. By convention
the current in the wire is taken to be in the direction of the flow of positive charge,
although it is actually negatively charged electrons, which flow along the wire in the
opposite direction.
A simple electric circuit consists of a battery as a voltage source, a switch and a
resistance - basically that is what is in a flashlight. The battery through processes that
need not concern us maintains a voltage difference between its terminals. With this
voltage difference, an electric charge experiences an accelerating force. When the switch is
made a conducting path is completed between the terminals of the battery and a current
flows in the wire as electrons respond to the accelerating force.
Oersted first established that wires carrying currents gave rise to magnetic fields.
He had noticed that when a current flowed in a wire, if a compass was placed close to the
wire it was deflected. Apparently, the first time he saw the effect it was by pure chance.
However, once he had seen the effect on the compass, he then mapped the magnetic field
lines around wires carrying electric currents and was able to show that they formed a
circular pattern around the wire. He also saw that the field lines were in a particular
orientation, which depended upon the sense of the current flow. The magnetic field lines
wrapped around the wire in a circular fashion, so that if one holds the thumb of the right
hand in the direction of the current then the natural curl of the fingers gives the sense of
the magnetic field lines.
It follows from the pattern of field lines around a length of wire that if we make a
loop of wire, we will produce a set of field lines equivalent to those of a bar magnet.
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Indeed whenever we wish to discuss the magnetic field of a magnet, we can consider it as
the magnetic field of a current loop.
As Ampère pointed out, we can think of all magnetic sources in terms of current
loops, so that the magnetic field of a magnet is the sum total of all the microscopic current
loops from all of its constituent atoms.
Magnetic fields and electric currents.
We have seen that just as gravitational fields act between masses, and magnetic
fields act between magnets, so also wherever there are static electric charges there are
electric fields and electric forces between the charges. Moreover, when an electric charge
is in motion, then a magnetic field is generated. Whenever an electric charge is in motion it
acts as a source of magnetic field. One might then ask - does a magnetic field act as a
source of an electric field?
This question was answered by Michael Faraday, whose experiments are some of
the most celebrated in all of science. Initially, he had been puzzled by the observation
that there appeared to be no induction in a circuit placed next to a circuit carrying a steady
current. To test this, he had placed a circuit carrying a strong current near to a second
circuit in which he had included a galvanometer. This was the most sensitive detector of a
current in those days, but Faraday saw no deflection, when a constant current was
flowing in the first coil. However, he noticed that when the current in the first circuit was
switched on, or off, the galvanometer did respond. He was smart enough to follow up
this unexpected result, which led to his recognition that although steady currents that gave
steady fields did not have an effect on a neighboring circuit, changing fields did.
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Thus he recognized that when the magnetic field in the vicinity of an electrical
circuit changes, then an electric current will flow in that circuit. Similarly if a magnet
moves with respect to a coil a current is induced, but if the magnet does not move with
respect to the coil no current is induced. The law of induction is named for Michael
Faraday, the Faraday law of magnetic induction. It also tells us that the electric current is
induced in such a way as to oppose the change of the magnetic field.
The Maxwell synthesis of electromagnetism.
Maxwell sought to express the results of Michael Faraday and of other
experimentalists in a mathematical form. He developed an analogy with the flow of water
and the flow of electricity and with it a mechanical model of the processes he sought to
explain. From all of this came the Maxwell synthesis, whose equations are known to all
scientists. We could simply write them in their beauty, but I was once told in connection
with a TV program that if you write a mathematical equation, you will immediately lose
in the neighborhood of 100,000 watchers given a typical science program. Let us try to
express the content of these beautiful equations in words and pictures. We consider the
equations in free space.
Equation 1 tells us that there are no electric charges present in free space, so there
is no electric field (E) originating from them.
The second is an equivalent statement for magnetism that there are no single
magnetic poles in free space acting as sources of magnetic fields (H).
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The third law expresses the fact that in the presence of a changing magnetic field
the electric field lines wrap themselves around the magnetic field lines so as to
oppose the change (fig A1.7).
The fourth does the same for a changing electric field, such as an electric charge in
motion, so that the magnetic field lines wrap themselves around the electric
current (fig. A1.6).
If we had written the last two equations in their mathematical form we would have that, a
constant appears, in both of them, about which there will be more immediately below.
The first two equations describe magnetostatics and electrostatics. The second two
contain electromagnetism. With material present and electrical and magnetic sources, the
equations become a little more complicated. Nevertheless that so many diverse
phenomena can be explained with just four equations remains a supreme example of the
economy in beautiful science. Of course, although it is true that the equations encompass
all electricity and magnetism and electromagnetism, it is their solutions that allow us to do
our homework problems. That can get complicated.
The constant in the last two equations mentioned above has the dimensions of
velocity. Maxwell saw that this had to be the speed of light. As recounted in an excellent
recent biography of Maxwell*, when he was working this out in a summer at Glenair, he
did not have a reliable number for the speed of light and had to wait until he returned to
Basil Mahon, “The man who changed everything - The life of James Clerk Maxwell”,
Wiley, 2003.
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London. Then to his delight he found agreement between his predicted value and those
observed. Maxwell is a shining light to all scientists not only because of his breathtaking
genius, which found expression in so many areas, but because he was such a kind and
generous man, loved by all, who knew him.
The force on a moving electric charge in a magnetic field.
The Lorentz law is another law of electromagnetism, which is important for our
story. It governs the behavior of a moving electric charge in a magnetic field. This law is
a little tricky in that the resulting force is not in the direction of either of the velocity of
the particle, or of the magnetic field. Both of these are of course examples of vectors, like
the gravity field. The resulting force is a third vector in the direction perpendicular to the
plane containing the velocity and the magnetic field. Thus, a charged particle moving in a
magnetic field experiences the force illustrated in figure A1.8. This can again be visualized
using the right hand with the thumb representing the direction of the velocity, the first
finger the field and then the second finger gives the direction of the force. A proton
experiences a force as illustrated, but an electron with its negative charge would experience
a force in the opposite direction, i.e. downward but still in the plane of the paper. This
law will turn out to be very important for us because it governs the motion of charged
particles entering the earth's magnetosphere, and the movement of electrically conducting
material in the earth's core.
2.5 Alternating currents .
In most of our discussion so far, we have only been concerned with steady fields
and currents. The notable exception was the Faraday law of induction, which related the
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change in the magnetic field to the induced electric current in a circuit. As the reader is
presumably well aware the electric currents, which are encountered for the most part in
everyday home appliances are alternating currents (AC). The instantaneous value follows
the simple pattern illustrated, which has the form of the trigonometric sine. The reason
that alternating currents are used is primarily because it is cost effective to transport
electricity at high voltages, while it is not convenient to operate household devices such as
the lamp on a desk with a kilovolt circuit. To change voltages between circuits, we use
transformers, which are alternating current devices.
What is it about alternating currents that makes this transformer action possible.
Building on Michael Faraday's experiments, we know that no current is generated in a
second circuit in the neighborhood of a circuit carrying a steady current. However, when
that current changes, such as when Faraday turned the current in the first circuit on, or
off, then a current was induced in the second circuit. It follows that if we arrange for the
current in the first circuit to be changing continuously then there will be continuous
induction of a current in the second circuit. In a transformer we increase the efficiency of
the transmission of power from the one circuit to the other by winding the two circuits in
a common magnetic core. The changing current in the primary produces a changing
magnetization of the core, which induces a current in the secondary. Transformers are
step down as in the figure, or step up, depending upon the ratio of the turns in the
primary and secondary circuits. The illustrated transformer is similar to one near my
house that is stepping down the high voltage low current supply to the house into the
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mains voltage within the house*.
From a practical point of view, we are interested in electrical circuits because they
do work for us - they toast the bread, or run the TV. In so doing they supply power, and
indeed we pay our electric bills in terms of how many kilowatt hours we have used, that
is how much power we have used for how long. The watt is a unit of power, which is the
rate of doing work, or expending energy. As we pay for the product of power and time
for which we have used the power, we evidently pay for the amount of work done by the
electricity, or the amount of energy supplied.
When we heat a piece of toast, or warm ourselves with an electric fire, the flow of
electricity in a wire has heated the wire, which has in turn heated the toast, or the room
and ourselves. The heat generated by the electric circuit has raised the temperature of the
toast, or the room, which requires so many calories of thermal energy to raise the
temperature each degree. Different household devices have different power levels, or
ratings. For example, an electric light bulb will use less power than an electric fire. Again
there are different wattages of electric light bulbs. Yet these devices all operate off the
same wall outlets, so that there must be something about them, which ensures that the
with other circuit elements, the relation is more complicated, but let us stay with the
simplest case. If you will forgive me, I would like to introduce two word equations here
------
* The figure and the discussion follow that given in James D. Livingston’s “Driving
Force The natural magic of magnets” Harvard press 1996. This is an excellent text on
magnetism for the general reader.
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related to the flow of current. There is a simple relation between resistance, voltage and
current, in a D.C. circuit, which every schoolboy and girl used to learn, called Ohm's law.
Voltage = Current x Resistance
The current, which flows in a circuit connected to a voltage source, such as a battery,
depends on the resistance. In an A.C. circuit, the impedance to current flow has to be
defined in a slightly more complicated manner, but the basic idea is similar - the current
which flows in the circuit is related to the voltage applied, via a number related to the
opposition to flow of the elements on the circuit.
The instantaneous power involved is found to be the product of the current and
resistance. However, it is the current squared, or multiplied by itself which governs the
heat dissipated, or the power generated.
Power = Current 2 x Resistance.
in the case of a DC circuit. Again in an AC circuit, things are a little more complicated.
However, if one wants to use an electric circuit to provide heat as in a toaster, or an
electric fire one needs power and one arranges for a relatively strong current to pass
through a resistance, but if one wants to transport electricity across country, while
minimizing the energy wasted on the way one wants a low current. We should use high
voltages and low currents to transport electricity, as Mr. Westinghouse realized at the end
of the 19th century to his considerable financial gain.
Electromagnetic radiation - light.
The crowning success of the Maxwell synthesis of electromagnetism in the 19th
century was the recognition that light is an electromagnetic radiation. He had seen that if
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the source of a magnetic field changed it propagated away from the source and generated
an electromagnetic ripple through space, which must be accompanied by a changing
electric field. To understand this, we have to develop the key idea of his, which permitted
his discovery.
We have already considered electrical circuits and seen how a voltage drives a
current around a circuit, which is connected continuously, but we have not thought about
what happens in a circuit such as the one illustrated in which the capacitor interrupts the
circuit. Maxwell argued that the capacitor being charged and the increasing electric field
between the plates, could be described in terms of a displacement current flowing between
the plates. If this were a true electric current, then a magnetic field would be generated in
circles round the current parallel to the plates of capacitor. Just such a magnetic field is
indeed found between the plates of the capacitor. If this magnetic field changes, it will
generate an electric field, so that if the capacitor is fed with an alternating supply the
electric fields will generate magnetic fields and the changing magnetic fields will give
electric fields in the immediate vicinity. Maxwell had seen that just as an electric current
flowed along wires, or through conductors of any shape, a current also flows in the
absence of material to conduct it and this he called the displacement current.
To understand the interpretation of light as an electromagnetic wave, consider the
antenna in the figure, which is being energized by a source of alternating current. This
gives rise to an oscillating dipole as illustrated and a wave of electric field spreads out
from the source, analogous to the pattern on the surface of water, when a stone is thrown
into water. The nature of the electric field can be determined from our earlier discussion
of the field of an electric dipole. Hence at the instants corresponding to the strengths of
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the dipole antenna illustrated by the sine wave the electric field will have the geometry
shown in the figure.
At a point in space successive fields of opposite sign will grow and fade as they
pass, Let us now consider what happens at the points along the equator of our diagram
and think about a small enough region that the wave can be regarded as planar. Because
the electric field is generated by an alternating power source, it must be continually
changing in magnitude. This electric field generates a magnetic field, which is itself
varying continuously. It is perpendicular to the electric field. Because the magnetic field
is continuously varying it induces an electric field. These two fields propagate away
riding on each other piggy-back from the source forming an electromagnetic wave. When
the wavelength of the electromagnetic wave is a few millionths of a meter, or a thousandth
of a millimeter, the resulting wave is visible light. However, there is a wide variety of
waves making up the electromagnetic spectrum.
Superconductivity.
In view of he fact that the principal instrument used in paleomagnetism is a
Superconducting Quantum Interference Device (SQUID), some discussion of
superconductivity is appropriate even though a satisfying discussion is again beyond the
scope of this book. Superconductivity arises because there is a very weak interaction
between electrons and the atomic vibrations of the lattice of a superconductor at low
temperature. Because they are acting as pairs, the electrons behave differently from their
behavior as single particles. A consequence of this is that at low temperature, these
Cooper pairs, as they are known, condense into the lowest energy state. Once this has
happened it extremely difficult for one pair to escape from this state.
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The first consequence of the electron pairs being strongly confined to the same
state is that there is no electrical resistance. This is because unlike the situation in normal
current flow, when individual electrons are stopped and eventually the current stops, it is
very difficult to separate one electron pair from the lowest energy state. The current
therefore flows unimpeded indefinitely. Our magnetometers use this principle to take the
current induced in the pick up coils to the sensor as a supercurrent.
The effect of superconductivity on magnetic fields is important to our story in
two ways. First, a magnetic field that exceeds some critical value for a particular material
destroys superconductivity. This is involved in the operation of the superconducting ring
used as sensors in the old RF SQUIDs. The second effect is that a magnetic field smaller
than the critical field is excluded from a superconductor. This is because as Faraday taught
us, whenever a magnetic field changes a current is induced to oppose that change. In a
superconductor, this current is sufficient to totally stop an infinitesimal field change.
Moreover, if a superconductor becomes a superconductor by for example lowering the
_______________________
An excellent discussion of superconductivity is given in the famous “Feynman Lectures
on Physics”, R.P. Feynman, R.B. Leighton and M. Sands, Addison-Wesley Publishing
Co. Superconductivity is covered in the form of a seminar.
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temperature, any magnetic field that is initially in the superconductor is expelled. This is
called the Meisner effect. These effects make superconductors magnetic shields and the
magnetometers used in paleomagnetism are maintained within a superconducting shield.
Units.
We need units to describe for example how strong magnetic fields are, just as we
need some form of currency to describe the financial value of an object. Units have
caused more than their fair share of confusion in electromagnetism. Indeed one
distinguished seismologist once confessed to me that he had wanted to study magnetism,
but never could understand the units In this book, I will limit discussions of units as much
as possible and only use them when it is necessary to give an indication of the magnitude
of an effect. Even then I will try to relate them in a simple way to something familiar in
everyday life. It should in any case be understood that units we use are a good deal more
arbitrary than is sometimes recognized. As with currencies, it really does not matter very
much, which units are chosen as basic units, as long as they are treated in a systematically
consistent manner. In the international system, the basic units are meters, kilograms and
seconds hence - MKS. It is questionable whether these units are anymore fundamental,
than others such as centimeters, grammes and seconds, or indeed some of the more
esoteric units beloved of theoreticians, but they have been recognized as more convenient.
I should perhaps be a little more careful here because there are certain systems of units
that are based directly on such qualities as the gravitational constant, the charge of an
electron and the speed of light that are in a sense absolute units because they are fixed by
fundamental constants. They are in this sense absolute unit systems. Nevertheless, it is
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an unfortunate fact that the units in electromagnetism have had a particularly checkered
history and have been the source of considerable confusion.
A final digression on magnetic fields and the interactions between magnets.
It is perhaps worth making another little digression here about the nature of
magnets and magnetic fields, even though it will take us briefly from the world of simple
explanations. For the ancients, such as Empedocles, the magnetic field was the result of
some sort of emanation from the magnet - effluvia. Millennia later despite all the
wonderful achievements of classical physics, it did not give a satisfying answer to the
very simple question “Why do two magnets attract each other?” We can say that there is
a force field between them, but how much greater an understanding do we have?
It took two 20th century developments to provide an answer to what appears to be a
very simple question. It will not be answered in detail here because it is once again
beyond the scope of this book, and indeed beyond your author. Yet to tempt the reader
go further, we note the key points. The first necessary recognition is that magnetic fields
are a relativistic effect of charges in motion. Thus there are not two fields, the magnetic
and the electric to be explained, but a single electromagnetic field. The second necessary
development was the weird and wonderful world of Quantum Electrodynamics (QED) 1.
The answer given by QED is that force in an electromagnetic field is explained by virtual
photons moving between the interacting particles. It must be admitted that the ideas of
QED The Strange Theory of Light and Matter, 1985, Richard Feynman, Princeton Press,
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QED make little appeal to common sense. However, the quantitative success of the ideas
of QED is so remarkable that as Feynman wrote
– “The theory of quantum
electrodynamics describes Nature as absurd from the point of view of common sense.
And it agrees with experiment. So I hope that you can accept Nature as She is – absurd.”
Conclusion.
This very rapid run through electricity and magnetism is not meant to
provide any profound understanding of the topic. It is equivalent to those old language
texts, such as “French without Tears” that might stop one from starving in France, but
would not permit the exchange of profound thoughts. The next stage can only be achieved
by a much greater effort, including the traditional working of problems to make sure of
that understanding. As has often been noted, physics is not a spectator sport.
Nevertheless, the coverage in this chapter will suffice for an understanding of most of the
material in this book.
Pages 21 5989
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App 01 Pictures.
Figure A1.1 Gravitational attraction of the earth on an apple and on the
moon produce accelerations towards the center of the earth, but because
the moon has a tangential velocity of v it remains in its orbit, whereas
the apple falls.
Figure A1.2 Magnetic field lines of a bar magnet illustrated by iron
filings.
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Figure A1.3 Attraction of magnet in an inhomogeneous
magnetic field.
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Figure A1.4 Alignment of a magnet in a homogeneous magnetic
field.
Figure A1.6 Magnetic field lines around a wire carrying
current. The current is coming up out of the page.
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Figure A1.7 The magnetic field of a dipole (small magnet) is equivalent
to the magnetic field of a current loop
Figure A1.7 - Magnetic induction of electric current.
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Force
Velocity
Field
Figure A.1.8
The Lorentz force.
Fig. A.1.9 Alternating current.
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Fig.A1.13 Principle of a transformer.
Fig. A.1.14 Propagation of electric field of an oscillating dipole.
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Figure A1.15. The propagation of an electromagnetic wave.
Fig. A1.16 The electromagnetic spectrum.