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

© 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 …

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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?

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Lightning strikes!

• Benjamin Franklin showed that the same process as involved in rubbing one thing on another gave rise to lightning.

– 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.

• Whatever they were, charges were very small.– 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.

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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 0.

• Maxwell was to show this constant is related to the speed of light.

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Related but not yet recognized• 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.

– 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.

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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.

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Magnets

• 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.

– 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.

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Moving charges affect magnets

• In 1820 Hans Christian Oersted observed that currents (moving electric charges) affected magnets much the same way as other magnets did.

– They exerted forces on the magnets.– He offered no explanation and no numerical measurements.

• 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.

– They introduced another constant to get the units right.– The equally famous 0/4

• Maxwell was to show that it too was related to the speed of light.

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The genius of Faraday• 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.

– 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

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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.

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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!!!!

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James Clerk Maxwell• 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.

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Maxwell’s symmetry and unification• 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!

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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:

• Remarkably, the speed of light was (00)-1/2 and did not have to be referenced to anything.

t

t

q

EJB

BE

B

E

000

0

0

God said and there was light.

© M. Bass

All sorts of electromagnetic waves

• 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.

– 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.– See the work of Hertz and Marconi for example.

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Victory• 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. – The only pre-Einstein theory that required no

relativistic corrections.• After all it is the theory of light.

• 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.

– Today we believe only 4 forces describe everything:• 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.