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Maxwell's Theory and the Displacement Current

Explore James Clerk Maxwell's contributions to electromagnetic theory, including his famous equations and the controversy surrounding the existence of the aether. Learn about the Michelson-Morley experiment and its impact on the development of relativity theory. Discover the modern-day application of Maxwell's ideas in the Laser Interferometer Gravitational-wave Observatory (LIGO).

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Maxwell's Theory and the Displacement Current

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  1. Chapter 14: Maxwell’s Theory By Katie Zerr and Kristin Walker Topics that will be covered: Electromagnetic Theory Displacement Current Michelson-Morley Experiment LIGO Precursors to Relativity

  2. 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

  3. More on Maxwell • Maxwell differed from his contemporaries in the nineteenth century • Faraday & Ampere contributed to Maxwell’s theories • Much of his important work was accomplished between the ages of 29 and 35

  4. 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.”

  5. Maxwell’s Contributions • Analysis of color perception • An explanation of Saturn’s rings • Analysis of the theory of fluids and solids • Helped father modern statistical mechanics and the molecular theory of gases • Theory of Electromagnetism – Maxwell’s equations

  6. Maxwell’s Equations • Gauss’s Law, no monopoles, Ampere’s Law and Faraday’s Law

  7. Prior to the Displacement Current Magnetic field generated solely by electric charge in motion – Ampere’s 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

  8. Displacement Current1st story Conflict could be resolved by modifying Ampere’s Law so that both electric current and displacement current generate the magnetic field:

  9. E - + 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

  10. 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

  11. 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 earth’s motion through the aether

  12. Michelson – Morley Experiment • Swimmers race across the river

  13. Michelson-Morley Animation • http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/mmexpt6.htm

  14. 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

  15. 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

  16. Precursors to Relativity (con’d) • 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 Poincaré’s principle but still left room for the aether

  17. 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

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