# Chapter 14: Maxwell’s Theory By Katie Zerr and Kristin Walker Topics that will be covered: Electromagnetic Theory Displacement Current Michelson-Morley.

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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

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

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

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.”

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

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

Prior to the Displacement Current Magnetic field generated solely by electric charge in motion – Ampere’s Law: It was also thought (and still is) that electric charge cannot be created or destroyed – the continuity equation:  Combined, give the result that the amount of electric charge at any particular place never changes – mathematical contradiction  B = (4  /c)j  J +  /  t = 0

Conflict could be resolved by modifying Ampere’s Law so that both electric current and displacement current generate the magnetic field: Displacement Current 1 st story

Displacement Current 2 nd story For a time dependent electric field, a material medium would become polarized, just as a dielectric does - + E  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

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

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

Michelson – Morley Experiment Swimmers race across the river

Michelson-Morley Animation http://galileoandeinstein.physics.virginia.ed u/more_stuff/flashlets/mmexpt6.htmhttp://galileoandeinstein.physics.virginia.ed u/more_stuff/flashlets/mmexpt6.htm

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

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

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

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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