Chapter 7: The Zeeman Effect
... Figure 7-29 shows a vector model diagram of the addition of L S to give J. The magnetic moments are indicated by the darker vectors. Such a vector model can be used to calculate the splitting of the levels, but since the calculation is rather involved, we will discuss only the results.19 Each ener ...
... Figure 7-29 shows a vector model diagram of the addition of L S to give J. The magnetic moments are indicated by the darker vectors. Such a vector model can be used to calculate the splitting of the levels, but since the calculation is rather involved, we will discuss only the results.19 Each ener ...
Fundamental of Physics
... 30. Two large parallel metal plates are 1.5 cm apart and have charges of equal magnitudes but opposite signs on their facing surfaces. Take the potential of the negative plate to be zero. If the potential halfway between the plates is then +5.0 V, what is the electric field in the region between the ...
... 30. Two large parallel metal plates are 1.5 cm apart and have charges of equal magnitudes but opposite signs on their facing surfaces. Take the potential of the negative plate to be zero. If the potential halfway between the plates is then +5.0 V, what is the electric field in the region between the ...
16-11. From Eq. (16.10), a general expression for a sinusoidal wave
... equilibrium, so its acceleration is zero. The y component of Newton’s second law yields T cos – mg = 0 and the x component yields T sin – Fe = 0. We solve the first equation for T and obtain T = mg/cos. We substitute the result into the second to obtain mg tan – Fe = 0. ...
... equilibrium, so its acceleration is zero. The y component of Newton’s second law yields T cos – mg = 0 and the x component yields T sin – Fe = 0. We solve the first equation for T and obtain T = mg/cos. We substitute the result into the second to obtain mg tan – Fe = 0. ...
Ch. 16 Electrical Energy and Capacitance
... A surface on which all points are at the same potential. No work is needed to move a charge at constant speed on an equipotential surface. Think of them as the contour lines on a topographical map. ...
... A surface on which all points are at the same potential. No work is needed to move a charge at constant speed on an equipotential surface. Think of them as the contour lines on a topographical map. ...
Ch. 16 Electrical Energy and Capacitance
... A surface on which all points are at the same potential. No work is needed to move a charge at constant speed on an equipotential surface. Think of them as the contour lines on a topographical map. ...
... A surface on which all points are at the same potential. No work is needed to move a charge at constant speed on an equipotential surface. Think of them as the contour lines on a topographical map. ...
45 Electric Fields - Mr. Smith`s Website
... The electric field intensity in the region outside the parallel plates is zero (except for a slight bulging of the field near the edges of the plates). ...
... The electric field intensity in the region outside the parallel plates is zero (except for a slight bulging of the field near the edges of the plates). ...
Electric potential energy and electric potential
... f. If this particle were placed at rest at the origin and then displaced slightly in the x direction, find its speed when it is at a very large distance from the origin. ...
... f. If this particle were placed at rest at the origin and then displaced slightly in the x direction, find its speed when it is at a very large distance from the origin. ...
Quantum Field Theory and Mathematics
... Gaiotto around 2010, we find that there should be a relation between the geometry of the instanton moduli space and the representation theory of infinite dimensional algebras. This conjecture was soon mathematically formulated, which got other mathematicians interested and inspired them to rigorousl ...
... Gaiotto around 2010, we find that there should be a relation between the geometry of the instanton moduli space and the representation theory of infinite dimensional algebras. This conjecture was soon mathematically formulated, which got other mathematicians interested and inspired them to rigorousl ...
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.