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Register a new userThe distribution of the electric current in a watt-balance coil
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In the watt balance experiments, separate measurements of the magnetic and electromotive forces in a coil in a magnetic field enable a virtual comparison between mechanical and electric powers to be carried out, which lead to an accurate measurement of the Planck constant. This paper investigates the three-dimensional nature of the coil-field interaction and describes the balance operation by a continuous three-dimensional model.
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A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field, minus the divergence of a tensor plus the curl of an axial vector. Such a separation is applied to the representation of electric current densities yielding a specific form of the effective polarization and magnetization fields which is also discussed in some details.
The purpose of this note is to make a brief analysis of the physical principles upon which two methods for relating the mass of an object to fundamental physical constants are based. The two methods are, namely, the watt balance method, and a still untested experimental technique based upon a superconductor electromechanical oscillator. We show that both these methods are governed by similar equations.
It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single PDE, which is derived from the Maxwells equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single PDE rather than with the complete Maxwells system, then the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.
An analysis of the influences of a high frequency (30 kHz) alternating current on the uniformity of the magnetic field (B) in an electromagnetic casting (EMC) mould is investigated by means of parametric numerical simulations where the induction current (Js) varies in the range of [1 to 10000 A]. The results show that values of the magnetic flux density along the casting direction (Bz) near the square mould corners are small, compared to those at the other locations where Js < 10000 A, and that the magnitude of Bz increases with an increased induction current (Js). However, it is shown that, for the EMC mould structure investigated in this paper, the variations of Js have no significant influences on the uniformity of the magnetic field, especially for the regions near molten steel level. Moreover, the effective acting region (Rbz) for the critical magnetic field (Bzc) is first introduced in this paper, which opens an interesting topic for future research.
Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in this work we try to show in detail, in a very didactic way, the demonstration of such a law. For this, the kinetic theory of gases is initially introduced. The good agreement of the Maxwell-Boltzmann velocity distribution law with experimental results and its applicability limit is also presented.
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