Lenz's Law Research Articles

TEACHING NOTES

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Near earth current meander (NECM) model of substorms

We propose that the appropriate instability to trigger a substorm is a tailward meander (in the equatorial plane) of the strong current filament that develops during the growth phase. From this single assumption follows the entire sequence of events for a substorm. The main particle acceleration mechanism in the plasma sheet is curvature drift with a dawn-dusk electric field, leading to the production of auroral arcs. Eventually the curvature becomes so high that the ions cannot negotiate the sharp turn at the field-reversal region, locally, at a certain time. The particle motion becomes chaotic, causing a local outward meander of the cross-tail current. An induction electric field is produced by Lenz's law, Eind=−∂A/∂t. An outward meander with Bz>0 will cause E×B flow everywhere out from the disturbance; this reaction is a macroscopic instability which we designate the electromotive instability. The response of the plasma is through charge separation and a scalar potential, Ees=−∇φ. Both types of electric fields have components parallel to B in a realistic magnetic field. For MHD theory to hold the net E∥ must be small; this usually seems to happen (because MHD often does hold), but not always. Part of the response is the formation of field-aligned currents producing the well-known substorm current diversion. This is a direct result of a strong E∥ind (the cause) needed to overcome the mirror force of the current carriers; this enables charge separation to produce an opposing electrostatic field E∥es (the effect). Satellite data confirm the reality of a strong E∥ in the plasma sheet by counter-streaming of electrons and ions, and by the inverse ion time dispersion, up to several 100 keV. The electron precipitation is associated with the westward traveling surge (WTS) and the ion with omega (Ω) bands, respectively. However, with zero curl, Ees cannot modify the emf e=∮E⋅dl=−dΦM/dt of the inductive electric field Eind (a property of vector fields); the charge separation that produces a reduction of E∥ must enhance the transverse component E⊥. The new plasma flow becomes a switch for access to the free energy of the stressed magnetotail. On the tailward side the dusk-dawn electric field with E⋅J 0 will cause injection into the inner plasma sheet, repeatedly observed at moderate energies of 1–50 keV. This same electric field near the emerging X-line will accelerate particles non-adiabatically to moderate energies. With high magnetic moments in a weak magnetic field, electrons (ions) can benefit from gradient and curvature drift to attain high energies (by the ratio of the magnetic field magnitude) in seconds (minutes).

LeChâtelier's Principle in the Sciences

LeChâtelier's principle of chemical equilibrium is actually a very general statement about systems in equilibrium and their behavior when subjected to external force or stress. Although one almost never finds mention of his name or law in other sciences, analogous principles and concepts do exist. In this note we examine some of the similar forms taken by this chemical principle in the fields of physics, geology, biology, and economics. Lenz's law in physics is an example of electromagnetic equilibrium and the geological principle of isostatic uplift concerns mechanical equilibrium. Both are strictly consequences of conservation of energy. LeChâtelier's principle deals with thermodynamic equilibrium and involves both the first and second laws of thermodynamics. The concept of homeostasis in biology and the economic law of supply and demand are both equilibrium-like principles, but involve systems in the steady state. However, all these principles involve the stability of the system under consideration and the analogies presented may be useful in the teaching of LeChâtelier's principle.

Electromagnetic Induction Rediscovered Using Original Texts

Some of Faraday's diary-entries from 1831 have been used frequently as starting point to introduce the phenomenon of electromagnetic induction. This has been done on various levels of knowledge and to pupils of different ages during the last 5 years. I try to let my pupils witness, how Faraday made his discovery, but to show as well, that we cannot infer from his notes, how he arrived at his ideas proper. Reading the original notes (in English), my pupils were expected to take out of it, what Faraday did at his lab, what apparatus he used and what his observations were. Why he did what he did was point of discussion later on. Just here, I expected, that my pupils learn a lot about the properties of electricity, of taking conclusions from experiment, of scientific methodology etc. In addition, we repeated some of Faradays experiments with modern quipment, realizing always to common surprise that the effects observed are extremely faint ones. Depending on knowledge, age and motivation of the group, Lenz's Law was rediscovered in succession. Here I myself try to find out, why Faradays initial mistake as for the direction of the induced current is likely to be overlooked even by the informed modern reader (myself included!). This may become part of a story, why this mistake of Faraday has found serious attention by historians of science only very recently. My approach was connected with group work with English courses, with the reading of more papers by Faraday and two times even with a visit of the Royal Institution at London. In any case, I always tried to put my pupils into the state of knowledge Faraday had at the time of his discovery before this unit, to make the process of discovery as correct as possible. For this claim is somewhat artificial at first glance, it may be an interesting point of discussion.

Effective dynamics of hot, soft non-Abelian gauge fields: Color conductivity and log(1/α)effects

B\"odeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) are logarithmically enhanced over previous estimates and take place at a rate per unit volume of order ${\ensuremath{\alpha}}^{5}{T}^{4}\mathrm{ln}(1/\ensuremath{\alpha})$ for small coupling. We give a simple physical interpretation of B\"odeker's qualitative and quantitative results in terms of Lenz's Law---the fact that conducting media resist changes in the magnetic field---and earlier authors' calculations of the color conductivity of such plasmas. In the process, we resolve some confusion in the literature about the value of the color conductivity and present an independent calculation. We also discuss the issue of whether the classical effective theory proposed by B\"odeker has a good continuum limit.

The correct application of Poynting's theorem to the time-dependent magnetosphere: reply to Heikkila

Abstract. Without Abstract

Comment on Lockwood and Davis, "On the longitudinal extent of magnetopause reconnection pulses"

Abstract. Lockwood and Davis (1996) present a concise description of magnetopause reconnection pulses, with the claimed support of three types of observations: (1) flux transfer events (FTE), (2) poleward-moving auroral forms on the dayside, and (3) steps in cusp ion dispersion characteristics. However, there are a number of errors and misconceptions in the paper that make their conclusions untenable. They do not properly take account of the fact that the relevant processes operate in the presence of a plasma. They fail to notice that the source of energy (a dynamo with E · J<0) must be close to the region of dissipation (the electrical load with E · J>0) in transient phenomena, since energy (or information) cannot travel faster than the group velocity of waves in the medium (here the Alfvén velocity VA). In short, Lockwood and Davis use the wrong contour in their attempt to evaluate the electromotive force (emf). This criticism goes beyond their article: a dynamo is not included in the usual definition of reconnection, only the reconnection load. Without an explicit source of energy in the assumed model, the idea of magnetic reconnection is improperly posed. Recent research has carried out a superposed epoch analysis of conditions near the dayside magnetopause and has found the dynamo and the load, both within the magnetopause current sheet. Since the magnetopause current is from dawn to dusk, the sign of E · J reflects the sign of the electric field. The electric field reverses, within the magnetopause; this can be discovered by an application of Lenz's law using the concept of erosion of the magnetopause. The net result is plasma transfer across the magnetopause to feed the low latitude boundary layer, at least partly on closed field lines, and viscous interaction as the mechanism by which solar wind plasma couples to the magnetosphere.

How things work: the physics of everyday life

How things work: the physics of everyday life

Interpretation of recent AMPTE data at the magnetopause

Phan and Paschmann [1996] have done a superposed epoch analysis of conditions near the dayside magnetopause and have found significant structure within the magnetopause current sheet itself. Among their many important results is that the electron temperature for an outward profile shows cooling of the solar wind plasma for the inner part followed by heating for the outer. Since these two cases are associated with E · J < 0 and E · J > 0, this pivotal result can be interpreted as evidence for a dynamo‐load combination. This was hypothesized by Heikkila [1982a] for the localized impulsive penetration of solar wind plasma through the magnetopause current sheet; the process involves an inductive electric field Eind given by Lenz's law around the current perturbation (the electromotive force) and a plasma response through charge separation caused by Eind, a process which is controlled by the normal component of the magnetic field Bn at the magnetopause. A dynamo is not included in the standard definition of reconnection, only the reconnection load. Another key result is a remarkable difference between inbound and outbound crossings of the normal component of plasma velocity υn. This can be understood on the basis of two complementary processes involving (1) a polarization electric field which does not depend on the movement of the magnetopause itself [Lemaire and Roth, 1978] and (2) the inductive electric field due to magnetopause erosion which does. These results have opened a new chapter on solar wind‐magnetospheric interaction. They demonstrate that the concepts of frozen‐in flow and of magnetic reconnection (as defined) are inappropriate at the magnetopause. Rather, the interaction of the solar wind plasma at the magnetopause depends on a localized pressure pulse whose effects vary greatly on the magnetic field topology, i.e. whether the magnetopause is a tangential or rotational discontinuity. Since the plasma is doing work, this is a form of viscous interaction.

Multiple reactions in inductors

In this paper, the importance of the high-order nested (recursive) reactions that can take place in lossy inductors is investigated. The inquisitive student may ask, What about the Faraday/Lenz reaction to the 'first' Faraday/Lenz reaction?-a matter about which textbooks are generally silent. It is shown here that the sinusoidal steady-state results for the current in a lossy inductor normally obtained by solving differential equations or performing phasor calculations can be reproduced exactly using Faraday's/Lenz's laws recursively, to infinite order. Thus no knowledge of differential equations nor of phasors is required to find the current, and the result practically demonstrates the connection between Faraday's/Lenz laws and circuit analysis. The case of a single sinusoid is analyzed, which by Fourier's theorem and linear superposition can in principle be generalized to any excitation. Moreover, the dynamic equations developed can be used directly for any excitation without appeal to Fourier decomposition. A typical nonsinusoidal initial-value problem, involving both transient and driving-function components, is solved as a further demonstration of the technique.

Using LEDs to demonstrate induced current

An experiment is described to prove the current produced by electromagnetic induction obeys Lenz's law.

Optical, magnetic, and single-particle excitations in the multiband Hubbard model for cuprate superconductors.

On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2\ifmmode\times\else\texttimes\fi{}2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x\ensuremath{\ne}0) a spectral Drude distribution around \ensuremath{\omega}=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet\ensuremath{\rightarrow}nonbonding oxygen transitions, again with relative weight \ensuremath{\sim}x.It is roughly centered at \ensuremath{\omega}\ensuremath{\sim}${\mathit{J}}_{\mathrm{Kondo}}$, where ${\mathit{J}}_{\mathrm{Kondo}}$ is the Kondo coupling and \ensuremath{\Delta} the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ``mid-infrared'' absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy \ensuremath{\sim}\ensuremath{\Delta}+${\mathit{U}}_{\mathit{p}\mathit{d}}$. They show a pronounced excitonic effect due to the p-d interaction ${\mathit{U}}_{\mathit{p}\mathit{d}}$ and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)--(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz's law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2${\mathit{J}}_{\mathrm{Kondo}}$, which should be detectable in experiment.

The ring-gyroscope: a search-coil for the magnetic-type gravitational field

The use of ring-gyroscopes to detect certain types of general relativistic gravitational field effects is considered using a generalised form of Lenz's law.

Electrical stability of bulk "S-shaped" negative differential conductivity media

As originally postulated by Ridley, bulk media exhibiting isothermal current-controlled negative differential conductivity (NDC) are shown to be unstable with respect to small fluctuations in the current density, leading to current density filamentation. In contrast to Ridley's arguments, however, we describe and elucidate the instability in terms of internal-induced magnetic flux. We show that Lenz's law does not apply to NDC points.

APPARATUS FOR TEACHING PHYSICS: Graphic Lenz's Law Effects in Model Armature Parts

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APPARATUS FOR TEACHING PHYSICS: Lenz's Law Demonstration

APPARATUS FOR TEACHING PHYSICS: Lenz's Law Demonstration

Simple Classroom Demonstration of Lenz's Law and the ac Induction Motor

Simple Classroom Demonstration of Lenz's Law and the ac Induction Motor

15. The neutral point discharge theory of solar flares. A reply to Cowling's criticism

The discharge theory has been criticized by Professor Cowling in §5·3 of The Sun, ed. Kuiper (Chicago[1]). A discharge theory requires the thickness of the accelerating layer to be only 5 m, which he finds unacceptable. This criticism is not soundly based, because no lower limit for the layer width is obtained from observation.Secondly, Cowling invokes Lenz's law: ‘the effect of induced currents is always to oppose the change to which they are due.’ Lenz's law needs verifying for conducting fluids, however, and though it is usually true, it is shown to be false when there is a neutral point. Since Lenz's law refers to electromagnetic induction, other effects such as the pressure gradient may be omitted in this test, and then a completely rigorous proof is possible: it is shown that in an ideal fluid which is perfectly conducting, perfectly compressible and inviscid, the current density at a neutral point must become infinite.The pressure gradient is irrelevant to Lenz's law, but it usually opposes any motion and should also be discussed. A physical picture suggests that the pressure gradient will not stop a vortical motion, but merely retard it. The related problem of equilibrium between the pressure gradient and the electromagnetic force may be discussed mathematically for the special case with two-dimensional symmetry. It is found that equilibrium requires an infinite current density at the neutral point. This is a subsidiary argument in favour of discharges at neutral points.