8.022pset10 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 10: Displacement current, Maxwell’s equations, radiation Post date: Thursday, April 29th Due date: Thursday, May 6th Be sure to write your name and section number on your pset Please staple multiple pages together 1. Purcell 9.6: Radiation’s ~ E and ~ B in SI units (15 pts). Be careful: Eq. (15’) of Purcell has a serious error! It should give ~ ∇· ~ E = ρ/² 0 . 2. Purcell 9.8: Wave in a box (15 pts). 3. Purcell 9.13: Relativistic transformation of wave’s Felds (15 pts). 4. Discovery of magnetic charge (10 pts): You discover magnetic charge. Congratulations. The units of magnetic charge density, μ , are chosen such that ~ ∇· ~ B = 4 πμ . (a) [5 pts] When this magnetic charge is in motion, there is a “magnetic current density” ~ L = μ~v . In analogy to electric charge density and electric current densities, write down the equation of continuity for magnetic charge. (b) [5 pts] What do Maxwell’s equations become with this new charge?
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