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Solution to HW Problems
Solution to HW Problems

... 2σa/(3ǫ0 ) + σa/(2ǫ0 ) = 7σa/(6ǫ0 ). (e) The polarization in each half slab is constant, so the volume bound charge is zero. The surface bound charge is given by P~ · n̂. Here we consider 3 surfaces, the top surface, the boundary between the two dielectric materials, and the bottom surface. At the t ...
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... electromagnetic induction, is at the heart of almost all electrical power generation worldwide. In addition to incredible technological importance, electromagnetic induction hints at a deep inter-relationship and symmetry between electric and magnetic fields that will explored more fully in later ch ...
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... the magnets contribute to the value at every point and this contribution decreases as the distance between the analyzed point and the magnet increases. At the center of the stack, all the magnets “work” under the same conditions. However, at the ends of the PPM, part of the magnetic field does not e ...
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... coherent (at least partially) after one revolution. Therefore, a mesoscopic ring at very low temperature is usually required. Second, to have a traveling wave, there has to be a phase advance (or lag) after one revolution. This can be achieved by threading a magnetic flux φ through the ring, so that ...
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Aharonov–Bohm effect

The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field (E, B), despite being confined to a region in which both the magnetic field B and electric field E are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wavefunction, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. This phase shift has been observed experimentally. There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested. An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, but this has no experimental confirmation yet. A separate ""molecular"" Aharonov–Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is ""neither nonlocal nor topological"", depending only on local quantities along the nuclear path.Werner Ehrenberg and Raymond E. Siday first predicted the effect in 1949, and similar effects were later published by Yakir Aharonov and David Bohm in 1959. After publication of the 1959 paper, Bohm was informed of Ehrenberg and Siday's work, which was acknowledged and credited in Bohm and Aharonov's subsequent 1961 paper.Subsequently, the effect was confirmed experimentally by several authors; a general review can be found in Peshkin and Tonomura (1989).
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