W9_parallel_resonance.eps
Week 9: Alternating Current Circuits 339 Problem 7. V 0 V 0 V 0 R R Rt Rt load load V 1 In this problem you must analyze the pro ...
340 Week 10: Maxwell’s Equations and Light Your answer for Z should remind you of parallel addition of resistors, using reactanc ...
Week 10: Maxwell’s Equations and Light I have also a paper afloat, with an electromagnetic theory of light, which, till I am con ...
342 Week 10: Maxwell’s Equations and Light Physicists usually rearrange them to make the equations connecting fields tosources ...
Week 10: Maxwell’s Equations and Light 343 In these equations, note well that: k= 2 π λ (790) is thewave numberof the wave, wher ...
344 Week 10: Maxwell’s Equations and Light The electromagnetic field also carriesmomentum, solving the dilemma of the “miss- in ...
Week 10: Maxwell’s Equations and Light 345 A direct consequence of this result is the death of classical physics. Classically, w ...
346 Week 10: Maxwell’s Equations and Light Ampere’s Law and the Maxwell Displacement Current As discussed at the end of week 8, ...
Week 10: Maxwell’s Equations and Light 347 S S C I +Q −Q I 1 Bφ 2 no current through S 2 Figure 138: A simple circuit and pair o ...
348 Week 10: Maxwell’s Equations and Light through a surface bounded by the curveC) is notinvariantwhen we vary the surfaceS in ...
Week 10: Maxwell’s Equations and Light 349 Note that I’ve chosen two simple surfacesS 1 andS 2 bounded byC– in fact, they are bo ...
350 Week 10: Maxwell’s Equations and Light Let us now guess that this invariant current is thecorrectone to use in Ampere’s Law, ...
Week 10: Maxwell’s Equations and Light 351 I C R r (r > R) Figure 140: A capacitor made up of two circular disks is being cha ...
352 Week 10: Maxwell’s Equations and Light (in the right handed direction around the current onto the disk as shown). If we choo ...
Week 10: Maxwell’s Equations and Light 353 magnetic fields make electric fields. Maxwell showed us thatat the same time, changin ...
354 Week 10: Maxwell’s Equations and Light Either Maxwell’s Equations arewrong, orclassical Newtonian mechanics itselfis wrong! ...
Week 10: Maxwell’s Equations and Light 355 Let us graph the fields on an arbitrary coordinate system and applyAmpere’s Law and F ...
356 Week 10: Maxwell’s Equations and Light Maxwell Displacement Current – this is where Maxwell’s contribution shines! ∮ B~·dℓ = ...
Week 10: Maxwell’s Equations and Light 357 If we substitute the second equation in for the last term, we get: d^2 Ex dz^2 =− d d ...
358 Week 10: Maxwell’s Equations and Light for example (you should verify this, obviously, bydoingit). So yes,By(z, t) is also a ...
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