Transcript 07. Electricity, Magnetism and Electromagnetics

ELECTRICITY,
MAGNETISM AND
ELECTROMAGNETICS:
JAMES CLERK MAXWELL:
SYMMETRY AND
UNIFICATION IN PHYSICS
Michael Bass
College of Optics and Photonics
University of Central Florida
© M. Bass
Electric charges
• Since the Greeks rubbed one thing on
another.
– around 700 BC someone was polishing
amber with cats fur and noticed that
things like straw and feathers were
attracted to it.
– the Greek word for amber is electron –
hence electric, electricity, electronics,
electron …
© M. Bass
Was it the amber itself?
• By 1600 Sir William Gilbert showed that this
property of attracting things when rubbed was
not a property of amber but was universal.
– Other stuff showed the same effect.
– Gilbert also showed that the earth was a magnet.
• The problem was that no one knew what was
being rubbed.
– Was it a fluid, an essence, or particles?
– Was the process of rubbing creating whatever was
responsible for the effect or was it moving something
around?
© M. Bass
Lightning strikes!
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Benjamin Franklin showed that the same process as
involved in rubbing one thing on another gave rise to
lightning.
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Whatever they were, charges were very small.
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He identified two types of charges and called them positive
and negative.
The only problem was that he got his signs wrong. The
charges that move about are negative not positive charges.
When there were many they could be thought of as resulting
in a continuous distribution in or on an object.
Later it was found that the smallest increment of
free charge that we can find in the universe is
that on the electron or 1.6 x 10-19 coulombs.
This is a description of things to come - charge was
considered quantized early.
© M. Bass
Quantify and make measurable
• Charles Augustin Coulomb (1736-1806)
• The law of force between point charges is
an inverse square law force.
– The electrostatic force had the same functional
form as Newton’s law of gravity
– Carl Freidrich Gauss would show this is due to
the fact that there are 3 dimensions to space.
• Introduced a proportionality constant to get
the units of force to be the same on both
sides of his equation.
– The famous e0.
• Maxwell was to show this constant is
related to the speed of light.
© M. Bass
Related but not yet recognized
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1803 - Thomas Young reported one of
the most brilliant and epochal
experiments ever.
The two slit interference experiment
gave incontrovertible proof that light
is wavelike.
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Keep in mind that Newton, the towering
figure of science, considered light to be
corpuscular.
97 years later Max Planck showed that
light has a particle like nature. Confusing
isn’t it?
This problem of duality is inherent in modern
quantum mechanics as we will discuss later.
For the time being however, light was
wavelike and Young had proved it.
Maxwell would show that light was
electromagnetic waves.
© M. Bass
What if charges moved?
• Clearly charges could move.
• What happened when charges moved?
– They exerted Coulomb’s force when static.
– What would be observed when they moved?
• How did they interact with each other, with
other objects and what effects would
result?
• To understand this we have to consider
magnetism.
© M. Bass
Magnets
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Magnets (lodestones are natural magnets) had
been known for centuries.
Since about 2000 BC the Chinese used them to
make compasses.
The word magnet comes from the name of a city
in Turkey, Magnesia, where the mineral
magnetite is found.
It was soon clear that magnets always have
both north and south poles.
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No mater how small you divided your magnet it always
had both a north and a south.
A modern way of saying this is to say that we have
never found a magnetic monopole, dipoles yes but
no monopoles.
© M. Bass
Moving charges affect magnets
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In 1820 Hans Christian Oersted observed that
currents (moving electric charges) affected
magnets much the same way as other magnets did.
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Also in 1820 Jean Baptiste Biot and Felix Savart, two
Frenchmen demonstrated that the magnetic force
due to a current was given by an inverse square law.
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They exerted forces on the magnets.
He offered no explanation and no numerical measurements.
They introduced another constant to get the units right.
The equally famous m0/4p
Maxwell was to show that it too was related to the
speed of light.
© M. Bass
The genius of Faraday
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In London (in a lab I visited in 1997) Michael
Faraday (1791-1867), an unschooled
bookbinder’s assistant, experimented with
magnets and currents.
In 1831 he observed that a moving magnet could
induce a current in a circuit.
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This is the inverse of Oersted’s observation.
Somehow electricity and magnetism were intimately
related!!!
This became Faraday’s law of induction and
ultimately one of Maxwell’s equations
© M. Bass
Other events of 1831
• Faraday also observed that a changing current
could, through its magnetic effects, induce a
current to flow in another circuit.
• If you spin a magnet inside a circuit it will generate
current – the electric generator.
© M. Bass
The real genius of Faraday
• Since he had no mathematical training
but thought geometrically, he
• invented the concept of fields of force.
– A geometric means of conceiving of what
his experiments were showing him.
• This concept, this interpretation of what
he saw is what set him apart from his
predecessors.
• It enables modern science!!!!
© M. Bass
James Clerk Maxwell
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James Clerk Maxwell had the
mathematical skills that Faraday
lacked and used them to become
the greatest theoretician of the
19th century.
He graduated Edinburgh
University at age 15 and became
a full professor at Aberdeen
University at age 17.
In the 40 years (1839-1879) of his
life he established the foundations
of electricity and magnetism as
electromagnetics, established
the kinetic theory of gasses,
explained the rings of Saturn
and experimented with color
vision.
© M. Bass
Maxwell’s symmetry and
unification
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Two rules governed electricity and two other rules
governed magnetism.
Maxwell noticed that in these laws the electric field and the
magnetic field appeared nearly symmetrically in the
equations.
For example, in Faraday’s Law a time varying magnetic
field gave rise to an electric field.
In Ampere’s law, as Maxwell modified it, a time varying
electric field gave rise to a magnetic field.
When made symmetric in electric and magnetic fields the
set of four equations described them both, they described
the subject we now call electromagnetism.
Electricity and magnetism had been
unified into electromagnetism!
© M. Bass
It had to be so
• Maxwell’s equations gave rise to a wave equation
for waves that propagated at the speed of light.
• Young had shown that light was a wave
phenomenon.
• Light had to be an electromagnetic wave and so:
E 
God said
q
e0
B  0
B
E  
t
  B  m 0 J  m 0e 0
and there was light.
E
t
• Remarkably, the speed of light was (e0m0)-1/2 and
did not have to be referenced to anything.
© M. Bass
All sorts of electromagnetic
waves
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Not only did Maxwell’s waves travel at the
speed of light, they were polarized just as is
light, they carried energy as does light and they
diffracted and interfered as does light.
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Faraday, by now an old man, had claimed light was a
transverse wave. He had been ridiculed for this.
Maxwell visited him to explain that he, Faraday, had
been right after all.
They also reflected and refracted.
Clearly, Maxwell’s electromagnetic waves were
a form of light.
Later it became clear that so were radio waves,
microwaves and many others.
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See the work of Hertz and Marconi for example.
© M. Bass
Victory
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Light was an electromagnetic wave.
Hertz and Marconi had shown that so were radio
waves.
Einstein was to show that Maxwell’s laws were
exactly valid in the relativistic case.
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The only pre-Einstein theory that required no
relativistic corrections.
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A stunning set of victories for the theory and
for the notions of symmetry and unification.
The first step towards unification of the different
forces that governed our universe.
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Today we believe only 4 forces describe everything:
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After all it is the theory of light.
Gravity; Electromagnetism; Weak nuclear; Strong nuclear
Maxwell’s principles, symmetry of form and
unification, are still in use today in science and
in our culture in general.
© M. Bass