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## Chapter 14: Maxwell’s Theory

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