Homogeneous dynamos and terrestrial magnetism

The main object of the paper is to discuss the possibility of a body of homogeneous fluid acting as a self-exciting dynamo. The discussion is for the most part confined to the solution of Maxwell’s equations for a sphere of electrically conducting fluid in which there are specified velocities. Solutions are obtained by expanding the velocity and the fields in spherical harmonics to give a set of simultaneous linear differential equations which are solved by numerical methods. Solutions exist when harmonics up to degree four are included. The convergence of the solutions when more harmonics are included is discussed, but convergence has not been proved. The simultaneous solution of Maxwell’s equations and the hydrodynamic equations has not been attempted, but a velocity system has been chosen that seems reasonable from a dynamical point of view. A parameter in the velocity system has been adjusted to satisfy the conservation of angular momentum in a rough way. Orders of magnitude are derived for a number of quantities connected with the dynamo theory of terrestrial magnetism. It is concluded that the dynamo theory does provide a self-consistent account of the origin of the earth’s magnetic field and raises no insuperable difficulties in other directions.

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XXVI.—On a Polarised Light Quantum

Proceedings of the Royal Society of Edinburgh ◽

10.1017/s0370164600022082 ◽

1927 ◽

Vol 46 ◽

pp. 306-313

Author(s):

J. M. Whittaker

Keyword(s):

Electromagnetic Waves ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Point Of View ◽

Light Quantum ◽

Electric Force ◽

Polarised Light

In the theory of radiation recently advanced by Sir J. J. Thomson it is supposed that electromagnetic waves and quanta are both present in a beam of light. The quanta, which are responsible for the photoelectric effects, are closed rings of electric force propagated in the direction normal to the plane of the ring. Professor Whittaker has discussed this conception from the point of view of Maxwell's equations, and has shown that it is consistent with them ; or rather with an extension of them in which a magnetic density μ analogous to the electric density ρ is introduced.

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A theory of magnetic-like fields for viscoelastic fluids

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.50 ◽

2019 ◽

Vol 865 ◽

pp. 460-491

Author(s):

Thibault Vieu ◽

Innocent Mutabazi

Keyword(s):

Magnetic Field ◽

Stress Tensor ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Viscoelastic Fluids ◽

Point Of View ◽

Viscoelastic Flows ◽

Maxwell Stress Tensor ◽

Viscoelastic Instability ◽

Theoretical Issues

We formulate the Oldroyd-B model for viscoelastic fluids in terms of magnetic-like fields obeying a set of equations analogous to Maxwell’s equations. In the limit of infinite relaxation time for the polymer, the polymeric stress tensor can be identified with the Maxwell stress tensor of a magnetic field. Away from this asymptotic case, the stress tensor of the polymer cannot be decomposed in terms of a tensor product of a magnetic field any more and several theoretical issues arise. We show that the analogy between the Oldroyd-B model and Maxwell’s equations can still be rigorously extended provided that one defines three magnetic-like fields obeying Maxwell’s equations with magnetic currents and charges. This solves the theoretical caveats and leads to a better understanding of the viscoelastic instability. In particular, we evidence a gauge symmetry which unifies some previous works, and we investigate several gauge choices. As an illustration we apply our method to viscoelastic Taylor–Couette flow but this theory of ‘viscoelastic fields’ is general and may be useful in a large variety of viscoelastic flows. The present study may also be of interest from the electromagnetic point of view, as it provides real systems possessing magnetic-like charges (monopoles) and currents.

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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Entropy ◽

10.3390/e23080987 ◽

2021 ◽

Vol 23 (8) ◽

pp. 987

Author(s):

Tomasz P. Stefański ◽

Jacek Gulgowski

Keyword(s):

Wave Propagation ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Momentum Conservation ◽

Point Of View ◽

Classical Electrodynamics ◽

Classical Solutions ◽

Systems With Memory ◽

Energy And Momentum ◽

With Memory

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

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A new point of view on the mathematical structure of Maxwell's equations

IEEE Transactions on Magnetics ◽

10.1109/20.250640 ◽

1993 ◽

Vol 29 (2) ◽

pp. 1315-1320 ◽

Cited By ~ 9

Author(s):

I.D. Mayergoyz ◽

J. D'Angelo

Keyword(s):

Maxwell’S Equations ◽

Maxwell's Equations ◽

Mathematical Structure ◽

Point Of View

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Note on the Antecedents of Clerk-Maxwell's Electrodynamical-Wave-Equations

Proceedings of the Royal Society of Edinburgh ◽

10.1017/s0370164600048574 ◽

1895 ◽

Vol 20 ◽

pp. 213-214 ◽

Cited By ~ 1

Author(s):

Tait

Keyword(s):

Maxwell’S Equations ◽

Wave Equations ◽

Maxwell's Equations ◽

Magnetic Force ◽

Elastic Solid ◽

Point Of View ◽

Polarised Light ◽

The Way

The first obvious difficulty which presents itself, in trying to derive Clerk-Maxwell's equations from those of the elastic-solid theory, appears in the fact that the latter, being linear, do not impose any relations among simultaneous disturbances. Thus, for instance, they indicate no reason for the associated disturbances which, in Maxwell's theory, constitute a ray of polarised light. Hence it appears that we must look on the vectors of electric and magnetic force, if they are to be accounted for on ordinary dynamical principles, as being necessary concomitants, qualities, or characteristics of one and the same vector-disturbance of the ether, and not themselves primarily disturbances. From this point of view the disturbance, in itself, does not correspond to light, and may perhaps not affect any of our senses. And the very form of the elastic equation at once suggests any number of sets of two concomitants of the desired nature, which are found to be related to one another in the way required by Maxwell's equations.

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