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## Lecure 8 Electromagnetism

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### Ampere's law for the magnetic field associated with any distribution of electric ... Ampere's law that allows time-varying electric fields to generate time-varying ... – PowerPoint PPT presentation

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Title: Lecure 8 Electromagnetism

1
Lecure 8 Electromagnetism Light
2
Lecture 8 Electromagnetism Light
• Maxwells unification of electricity, magnetism,
light
• Need to add time-rate of change of electric field
to Amperes law for current as source of magnetic
field.
• Possibility in vacuum (absence of charges and
currents) for time-varying magnetic fields and
time-varying electric fields to sustain each
other light as an electromagnetic wave.
• Generation of light via the acceleration or
deceleration of electric charges.
• Conflict between Maxwells theory and Newtonian
physics.

3
Summary of Electricity Magnetism Before Maxwell
4
James Clerk Maxwell (1831-1879)
• Found a way to give precise mathematical
expression to
• Gilberts discovery of no magnetic monopoles
(magnetic field lines neither begin nor end on
magnetic charges).
• Coulombs law for the electric field associated
with any collection of electric charges.
• Amperes law for the magnetic field associated
with any distribution of electric currents.
• Faradays law of induction that time-varying
magnetic fields can generate time-varying
electric fields.
• Discovered four equations given above are
inconsistent with Franklins law of the
conservation of electric charge unless one adds a
term in Amperes law that allows time-varying
electric fields to generate time-varying magnetic
fields, even in the absence of electric currents.

5
Light as an Electromagnetic Wave
• Time-varying B gives rise to time-varying E, even
in the absence of charge whereas time-varying E
gives rise to time-varying B, even in the absence
of current.
• Can time-varying E and B sustain each other in a
vacuum absent of any charges or currents? If so,
what are the properties of the resulting
electromagnetic fields?
• Maxwells answer Disturbances that propagate at
the speed of light, c 300,000 km/s. In other
words, light is an electromagnetic wave!

6
Maxwells Picture of Light as an Electromagnetic
Wave
7
Classical Picture Why an Accelerated Charge
8
Conflict between Electromagnetism and Newtonian
Mechanics
• As schoolboy of 16, Albert Einstein (1879-1955)
wonders what an electromagnetic wave will look
like if one were to race alongside it at the
speed of light c.
• Answer a wave that oscillates in space, but not
in time.
• But Maxwells equations in a vacuum have no such
solutions! Only nontrivial solutions that are
independent of time in a vacuum are constant E
and B, not E and B wavy in space.
• Because nothing in Newtonian mechanics forbids
one from having a speed equal to c, Einstein
decides either Maxwell must be wrong, or Newton
must be wrong
• Einstein thinks Maxwells equations are too
beautiful to be false, and he boldly speculates
that it must be Newton who is wrong!
• Thus, it must not be possible for anyone to race
at the speed of light! The reason why is the
subject of Einsteins theory of special
relativity, which is the topic of a future
lecture.

9
Discovery of the Electron
• J. J. Thomson (1856-1940) experiments with
electric discharges and cathode ray tubes (like
fluorscent lamps).
• Bent beams with strong magnetic fields B.
• Amount of bending depends on charge to mass
ratio q/m.

• B pointing into page
• Strongest bending by particles (electrons) with
• q/m e/m (Thomson only measured ratio).
• Separate measurement of e by Milliken
(1868-1953) in famous oil drop experiment.

q gt 0
q lt 0
e
10
Radiation from a Suddenly Stopped Charge
11
Discovery of X-Rays by Roentgen (1845-1928)
12
The Electromagnetic Spectrum
13
Summary Unification of Electricity, Magnetism,
Light
• For millennia, electricity, magnetism, light
were studied as separate curiosities, devoid of
many practical applications (apart from the
magnetic compass).
• Then, in the space of a few centuries, the
efforts of many scientists began to reveal
quantitative relationships.
• The effort culminates in the great synthesis by
Faraday and Maxwell, which results in a
comprehensive theory of the related phenomena, as
well as many practical applications (power
generation by alternating currents, artificial
sources of light, radio and television,
telephone, telegraph, wireless communication,
etc.).
• Interestingly, the unification of these separate
branches of science brings them into conflict
with other fundamental branches of science, in
this case, Newtonian mechanics. The resolution
of the resulting conflict, in Einsteins theory
of special relativity, opens new frontiers
concerning concepts that we had heretofore taken
for granted, in this case, the nature of space
and time.
• Will this process of synthesis, unification, and
opening of new frontiers ever stop? Is the
process of fundamental scientific discovery
finite or infinite?