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Lecure 8 Electromagnetism


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

Lecure 8 Electromagnetism Light
Lecture 8 Electromagnetism Light
  • Maxwells unification of electricity, magnetism,
  • Need to add time-rate of change of electric field
    to Amperes law for current as source of magnetic
  • 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

Summary of Electricity Magnetism Before Maxwell
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.

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!

Maxwells Picture of Light as an Electromagnetic
Classical Picture Why an Accelerated Charge
Radiates Light
Conflict between Electromagnetism and Newtonian
  • 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

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
Radiation from a Suddenly Stopped Charge
Discovery of X-Rays by Roentgen (1845-1928)
The Electromagnetic Spectrum
Summary Unification of Electricity, Magnetism,
  • 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,
  • 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?
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