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III
III

Document
Document

January 2009
January 2009

Chapter 19 Electric Potential Energy and the Electric Potential
Chapter 19 Electric Potential Energy and the Electric Potential

GonzalesMestres
GonzalesMestres

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... Net force is the vector sum of forces from each charge ...
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... 5) Two equally charged balls are 3 cm apart in air and repel each other with a force of 40 μN. Compute the charge on each ball. 7) Four equal point charges of +3μ C are placed at the four corners of a square that is 40 cm on a side. Find the force on any one of the charges. 8) Four equal magnitude p ...
The Electromagnetic Shift of Energy Levels
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... 1.2x10⁶ m/s parallel to the electric field, as shown below. (a) Calculate the work done on the electron by the field when the electron has travelled 2.5 cm in the field. (b) Calculate the speed of the electron after it has travelled 2.5 cm in the field. (c) If the direction if the electric field is ...
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... Several interesting paradoxes related to parallel capacitors had been raised[1][2][3][4]. No matter which method which we use to analysis a physical system, as long as we are on the right tracks, the equations describing the system should be the same. Because the nature of the physical system should ...
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... When it is displaced to the right, the force will be directed to the left and so the mass will move back. It will overshoot the equilibrium position of a and move past it to the left. Once there, the net force will now be directed to the right and so the mass will keep oscillating. ...
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... e” and m” are never zero except at w = 0. However, they may be very small e”<<|e’| Then, neglect absorption. Now we can talk about definite internal energy as in the static case, except now it is not constant. In static case, these were real constants independent of w ...
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Calculate amount of work - worksheet File

... Background: This may be your first true worksheet. Get it? Work = Force x Distance. Work results in a change in energy. Work is done if an object’s kinetic energy changes. Work is done if gravitational potential energy of the object changes. Imagine sliding a book across a table at constant speed; t ...
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Casimir effect



In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.
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