no worries for theoretical physics

**Tóm tắt** Ampère's law establishes the connection between electric current (as described by current density, j) and the resulting magnetic field (H). It states that the circulation of the magnetic field around a closed loop is equal to the current through the surface bounded by the loop. The magnetic field of a current-carrying wire is given by the Biot-Savart law, which expresses the inverse-proportional relationship between the field and the distance from the wire, as well as the dependence on the current and the orientation of the wire. The magnetic field of a current loop can be equivalently described using an equivalent magnetic dipole, with the magnetic moment proportional to the current and the area of the loop.

Ngày tải lên: 06/07/2014, 17:20

... Sontay Highway, Hanoi,Vietnam, Nguyen Thanh Hai1 Hanoi University of Technology, 01 Dai Co Viet Road, Hanoi, Vietnam and The Abdus Salam International Centre for Theoretical Physics, Trieste, ... INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS CALCULATION OF THERMODYNAMIC QUANTITIES OF CUBIC ZIRCONIA BY STATISTICAL MOMENT METHOD Vu Van Hung Hanoi National Pedagogic University, Km8 Hanoi- Sontay ... can form cubic, tetragonal and monoclinic or orthorhombic phases at high pressure Pure zirconia undergoes two crystallographic transformations between room temperature and its melting point: monoclinic

Ngày tải lên: 12/04/2021, 22:56

... presently used for many purposes. 14.2 Coriolis Force and Weather Pattern Apart from elevator forces, Coriolis forces are perhaps the most important inertial force. In contrast to centrifugal forces ... also by a wealth of nontrivial empirical results. As a consequence, for decades they have belonged to the canonical wisdom not only of university physics, but also of school physics and gradually ... where ˆz denotes the axis of rotation, we have F  Coriolis = −2m t ·ωv x e y , 98 14 Accelerated Reference Frames i.e., a force directed from north to south. As a consequence, in the northern

Ngày tải lên: 06/07/2014, 17:20

... One should not forget to write the “dot” for the scalar multiplication (also called “dot product”) of the vectors v 1 and v 2 , since for example c := ∇v (i.e., without ·), would not be a scalar ... should note the different powers of c in the last terms of (16.3) and (16.4). Another example illustrating the differences between the two equivalent measuring systems is the equation for the force ... and refers to the phenomenon of frictional or static elec- tricity. It was well known in ancient times that amber can be given an electric charge by rubbing it, but it was not until the eighteenth

Ngày tải lên: 06/07/2014, 17:20

... also applies for Newton’s gravitational forces, is often erroneously assumed to be self-evident. However for other forces, such as those generated by nuclear interactions, it does not apply at ... theory which is formally rather similar to Maxwell’s electrodynamics but describing nuclear forces, are non-linear,sotheprinciple of superposition is not valid there. 17.1.2 Integral for Calculating ... (17.16) Therefore one always obtains the following relation for the total differen- tial dφ: dφ =gradφ · dr = 3  i=1 ∂φ ∂u i du i . This formulation of the vectors dr and gradφ does not depend

Ngày tải lên: 06/07/2014, 17:20

... Therefore, since ∇ 2 w =0 wehave  Is (∇w) 2 dV =0; 17.1 Electrostatic Fields in Vacuo 131 as a consequence ∇w ≡ 0 everywhere (apart from a set of zero measure). Therefore, it is not now the ... calculation can be performed for an electric quadrupole.The corresponding array of charges consists of two opposite dipoles shifted by a vector b. 11 The Taylor expansion must now be performed up to second ... decided if one knows which system of units is being used.) 17.2.4 Multipole Moments and Multipole Expansion The starting point for this rather general subsection is the formula for the potential

Ngày tải lên: 06/07/2014, 17:20

... etc. 159 b) The transformer The index 1 above refers to the number of windings for a single solenoid. Now consider a second solenoid of equal length wrapped around the first solenoid and possessing ... inter alia the Lorentz force, i.e., not only b), but also a). 2 Shortly before Einstein’s special theory of relativity Lorentz also formulated his famous Lorentz transformations. 156 19 Maxwell’s ... solenoid 2 are assumed to remain open, i.e., no current flows through solenoid 2, in contrast to solenoid 1, through which a current I 1 flows. The magnetic field H 2 in the interior of solenoid

Ngày tải lên: 06/07/2014, 17:20

... phenomenological relaxation time corresponding to scattering processes. 1 In the case of a linear relation (e.g., between E and D or B and H) the derivative is non-formal; otherwise (e.g., for ... height U (0) G /R, and for weak damping (i.e., for sufficiently small values of R) it decays very quickly as a function of ω, for very small deviations from ω = ω 0 ; i.e., for ω ± := ω 0 ± ε, where ... . For sufficiently small R (see below) this yields a sharp resonance at the resonance frequency ω 0 := 1 √ L · C . For this frequency the current and the voltage are exactly in phase, whereas for

Ngày tải lên: 06/07/2014, 17:20

... transformations for the x-andt-components of the Minkowski four-potential ˜ A, for a transition between different inertial frames the following “more complicated” Lorentz transformations for elec- ... equations does not change, if E is transformed into cB,andB into −c −1 E  (E,cB) →  0, +1 −1, 0  E cB  . To be more precise, if in equation (20.14) B is transformed into −D and E is transformed ... MeV, characteristic for the electron shell of atoms, whereas for γ-radiation one is dealing with excitations of nuclei, i.e., ΔE ≈ 1MeVup to1GeV. Fourthly, Planck’s formula for black-body radiation:

Ngày tải lên: 06/07/2014, 17:20

... has to be used, then Planck’s formula can be generalized. For example, for the excitations of so-called quasi-particles resembling photons, e.g. for “phonons” or “magnons” (the quanta of sound waves ... considered as a particle phenomenon (Newton) or a wave phenomenon (Huygens). The answer is “both” (→ wave- particle duality, see Part III). According to Einstein (1905, → Nobel prize 1921) electromagnetic ... magnons in ferromagnets and ω(k)=ω p + b · k 2 for plasmons,whereω p is the plasma frequency and b a positive factor.) Thus in analogous manner to that for photons one obtains different results for

Ngày tải lên: 06/07/2014, 17:20

... which increases monotonically from (I/I 0 )=0forw = −∞ (roughly ∼ 1/w 2 ) up to a maximum amplitude (I/I 0 ) ≈ 1.37 for w ≈  3π 4 (The characteristic length scale for this monotonic increase ... and which is therefore not as small as one might naively believe (in particular it can be significantly larger than the characteristic length λ 2 for the above- mentioned monotonic increase), ... subject cannot be treated in detail here.) For photographic records the blackening is proportional to the intensity, i.e., one loses the information contained in the phase of the wave. Long before

Ngày tải lên: 06/07/2014, 17:20

... gained the Nobel prize in 1921; and (iii) (a lesser well-known work) he dealt with Brownian motion, [35], where he not only explained the phenomenon atomistically, but proposed a basic relation between ... on the H-atom (e.g., the Ryd- berg formula and the corresponding spectral series) not only qualitatively or approximately, but even quantitatively. One therefore tried to explain the spectral ... Therefore one writes compactly ˆp x =(/i)(∂/∂x) . More precisely, one assumes that the operator corresponding to an observable ˆ A is not only Hermitian, i.e., ψ 1 | ˆ Aψ 2  =  ˆ Aψ 1 |ψ 2  for

Ngày tải lên: 06/07/2014, 17:20

... continuous and monotonically nondecreasing, but nowhere differen- tiable function g(λ) (the usual above-mentioned continuous contribution is obtained in the differentiable case g(λ) ≡ λ). For a pure ... the differential expression for ˆp x has no eigenfunctions for the interval, in the latter case it has a complete set. 216 24 Quantum Mechanics: Foundations 24.3 The Canonical Commutation Relation ... 2 . Nowadays one might update the question for contemporary purposes. For example we could assume that Schr¨odinger’s proverbial cat carries a bomb attached to its collar 19 , which would not

Ngày tải lên: 06/07/2014, 17:20

... model” for the mutual binding of a neutron and proton in the deuteron nucleus the depth V 0 is just deep enough to generate a bound state, whereas for a“di-neutron” it is just not deep enough.) Nodal ... ψ 0 , has no “nodes” (i.e., no zeroes) at all (between the interval limits, i.e., here for −∞ <x<∞). In contrast, an eigenstate ψ n ,forn =1, 2, , if existent, has exactly n nodes. If parity ... =2ν 0 +1. If it were not terminated, i.e., if for all non-negative integers ν the identity ε =2ν + 1 were violated, then v(ξ) would diverge for |ξ|1(forevenparity, i.e., for [a 0 =0,a 1 = 0],

Ngày tải lên: 06/07/2014, 17:20

... http://www.feedbooks.com Strictly for personal use, not use this file for commercial purposes Transcriber's Note: This etext was produced from Amazing Stories April-May 1953 Extensive research did not uncover any ... Hoyt to argue with at the same time, was all for putting him on the ship and asking Earth for another intern But Miss Dupont talked him out of it For no discernible reason other than loneliness, ... I know my way around this poor little wretch of a building Not much like Earth hospitals, is it?" He headed for the medical supply room, adding just before he went in, "A lot can be said for...

Ngày tải lên: 15/02/2014, 00:20

... & PDEs of Physics 8.1 Nonlinear ODEs: Exact Methods 8.1.1 Jacob Bernoulli and the Nonlinear Diode 8.1.2 The Chase 8.1.3 Not As Hard As It Seems 8.2 Nonlinear ... methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to ... men Who knows if a well-prepared soup was not responsible for the pneumatic pump or a poor one for a war? G C Lichtenberg, German physicist, philosopher (1742–99) Chapter Linear ODEs of Physics...

Ngày tải lên: 17/03/2014, 14:25

... functions and hence to theoretical physics of the usual kind We not know for certain that space and time are quite as smooth as this, but at least there is no evidence for any granularity down ... Contents vii Forces, Connections and Gauge Fields 8.1 Electromagnetism 8.2 Non-Abelian Gauge Theories 8.3 Non-Abelian Theories and Electromagnetism 8.4 Relevance of Non-Abelian Theories to Physics ... devoted, for example, to gravitation and cosmology or elementary particle physics are required to give a broad view of the phenomenological aspects of their subjects, which leaves little room for...

Ngày tải lên: 24/04/2014, 17:10

... Inserting the form (1.154) for the solution, we find that κ= and hence mV h2 ¯ V E=− m h ¯ (1.159) (1.160) Thus for E < there is a unique solution for E, and hence a single bound state For E > 0, ... (1.86) and similarly for ∆B The expectation value is over some arbitrary state vector This is the generalised uncertainty principle, which implies that it is not possible for two non-commuting ˆ observables ... is a non-zero ˆ ˆ real number (times the unit operator), then A and B cannot possess any simultaneous eigenstates Problem 6: Prove (1.85) ˆ If the eigenvalues of A are non-degenerate, the normalised...

Ngày tải lên: 24/04/2014, 17:13

... fascinating issues of theoretical physics During his scientific career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form For this reason, as ... essential period, however, for theoretical physics at Wroclaw University is the period 1970–84 when Jan Lopusza´ski was the Director of the Institute for Theoretical Physics n On one side he promoted ... University and the head of theoretical physics there, Prof C.N Yang, Nobel Prize winner in 1957 In the late 1970s at least half of the members of the Institute for Theoretical Physics at Wroclaw University...

Ngày tải lên: 24/04/2014, 17:16

... laws 33, 36, 39 nodal theorem 226, 240 Noether’s theorem 49, 50 non-additivity of the partial pressures for real gases 414 non-autonomous 86 non-degenerate perturbation theory 262 non-existence ... 126 Lorentz force 27, 45, 153, 155, 217, 295 force (mksA versus cgs) 112 gauge 165, 176 transformations 56 transformations for the electromagnetic fields 177 force 60 gauge 166 transformations ... 129 non-integrable systems 85 non-linearity (e.g of the chromodynamic equations for nuclear physics) 120 non-locality of quantum mechanics (singlet decay) 281, 295 non-perturbative terms 263 non-reality...

Ngày tải lên: 06/07/2014, 17:20