Maxwell

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Chapter 14 Maxwells Theory
By Katie Zerr and Kristin Walker
Topics that will be covered Electromagnetic
Theory Displacement Current Michelson-Morley
Experiment LIGO Precursors to Relativity
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James Clerk Maxwell

• Born in Edinburgh, Scotland in 1831
• Attended Edinburgh Academy, The University of
  Edinburgh, and Cambridge University
• Published by the young age of 14

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More on Maxwell

• Maxwell differed from his contemporaries in the
  nineteenth century
• Faraday Ampere contributed to Maxwells
  theories
• Much of his important work was accomplished
  between the ages of 29 and 35

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Aether

• Appendix of Chapter 13
• When we observe one body acting on another at a
  distance . . . we generally inquire whether there
  is any material connection between the two bodies
  . . . we prefer to explain the action by means of
  these intermediate connections, rather than to
  admit the notion of direct action at a distance.

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Maxwells Contributions

• Analysis of color perception
• An explanation of Saturns rings
• Analysis of the theory of fluids and solids
• Helped father modern statistical mechanics and
  the molecular theory of gases
• Theory of Electromagnetism Maxwells equations

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Maxwells Equations

• Gausss Law, no monopoles, Amperes Law and
  Faradays Law

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Prior to the Displacement Current
Magnetic field generated solely by electric
charge in motion Amperes Law
?? B (4?/c)j
It was also thought (and still is) that electric
charge cannot be created or destroyed the
continuity equation
?? J ??/?t 0

• Combined, give the result that the amount of
  electric charge at any particular place never
  changes mathematical contradiction

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Displacement Current1st story
Conflict could be resolved by modifying Amperes
Law so that both electric current and
displacement current generate the magnetic field
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Displacement Current 2nd story
For a time dependent electric field, a material
medium would become polarized, just as a
dielectric does

• For a constant E field, each pair of charges
  soon equilibrates as shown above
• If the E field varies with time, then the charge
  configurations are constantly in motion
  displacement current

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The Final Classical Theory

• 1865 paper A Dynamical Theory of the
  Electromagnetic Field did not discuss vortices
  and idle wheels
• Classical mechanics was used as model
• After consistent defeat, mechanical models
  abandoned
• Electromagnetic theory distinct branch of physics

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Albert Michelson (1852-1931)

• American experimental physicist
• Devoted his life to making extremely accurate
  measurements of the speed of light
• Nobel Prize in Physics in 1907 for his efforts
• 1887 collaborated with Edward Morley to perform
  an experiment sensitive enough to detect the
  earths motion through the aether

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Michelson Morley Experiment

• Swimmers race across the river

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Michelson-Morley Animation

• http//galileoandeinstein.physics.virginia.edu/mor
  e_stuff/flashlets/mmexpt6.htm

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LIGO

• LIGO stands for Laser Interferometer
  Gravitational-wave Observatory
• Similar apparatus to Michelson-Morley
• Run into same problem- trying to block out high
  frequency sounds that disrupt results
• They hang apparatus while Michelson and Morley
  suspended theirs in mercury

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Precursors to Relativity

• FitzGerald (1851-1901) could avoid negative
  result of Michelson-Morley experiment
• Contraction hypothesis was independently
  postulated by Hendrik Lorentz
• Lorentz manipulated equations and are called
  Lorentz transformations today
• Lorentz-FitzGerald contraction hypothesis

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Precursors to Relativity (cond)

• Poincaré postulated that
• optical phenomena depend only on the relative
  motions of the material bodies
• He questioned the existence of aether
• In 1904 he determined his principle of relativity
• Lorentz came up with a theory of electrons
  consistent with Poincarés principle but still
  left room for the aether

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Conclusion

• Maxwell provided us with modern physical and
  mathematical equations
• Many contributions to physics even though his
  belief in the existence of aether was not valid
• Michelson-Morley experiment proved aether wrong
• LIGO today uses similar apparatus and encounters
  similar problems