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FIELD THEORY 1. Consider the following lagrangian1
FIELD THEORY 1. Consider the following lagrangian1

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Slide 1
Slide 1

exercises.electrostatics.2
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... of length L, as shown in Fig. 2. Each sphere has the same charge q. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Show that if the angle θ is small, the equilibrium separation d between the spheres is d  (q 2 L / 2o ...
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... and will not change unless the rock is heated. Sensitive instruments can then be used to measure the magnetic orientation in the rocks. Using several lava flows from the same time period enables geologists to locate the magnetic poles for that particular time. Although we don’t know for sure, we thi ...
the quantum mechanical potential for the prime numbers
the quantum mechanical potential for the prime numbers

... The plot of this function is drawn in Fig. 1 (with E0 = 0): the series (??) rapidly converges to a limiting function, which can be regarded as the potential W(x), solution of the problem5. The existence of a potential which admits all the prime numbers as its only eigenvalues has some important imp ...
Physics 2102 Spring 2002 Lecture 2
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When a coil of wire and a bar magnet are moved in relation to each
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... Ex. 5 - A coil of wire consists of 20 turns, each of which has an area of 1.5 x 10-3 m2. A magnetic field is perpendicular to the surface of the loops at all times. At time t0 = 0, the magnitude of the magnetic field at the location of the coil is B0 = 0.050 T. At a later time t = 0.10 s, the magni ...
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... radius c . Find the electric field and electric potential at a point a distance r from the center separately for the four regions r  a, a  r  b, b  r  c, c  r when the total charge on the outer shell is (a) zero, (b)  Q , and (c) Q . 11. Two spherical conductors are widely separated. One has ...
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5.physics

... (ii) Loop rule: The algebraic sum of the changes in potential around any closed loop involving resistors and cells in the loop is zero. Applying Kirchhoff’s rules for the loop ABCD and for the loop DCFE, we get, 40I3 + 20I1 = -40 12 + 2I3 =6 Applying Junction rule at D, 13 = I1 + I2 Solving the abov ...
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qq29
qq29

... Answer: (c). Because all loops enclose the same area and carry the same current, the magnitude of μ is the same for all. For part (c) in the image, μ points upward and is perpendicular to the magnetic field and τ = μB, the maximum torque possible. For the loop in (a), μ points along the direction of ...
Document
Document

... on a charge is proportional to the charge’s velocity relative to the field. If the charge is stationary, as in this situation, there is no magnetic force. ...
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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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