Motional Emf Research Articles

Electric and magnetic fields as explicitly observer dependent four-dimensional vectors and their Lorentz transformations according to Minkowski - Ivezić

In this paper a geometric approach to the special relativity (SR) is used that is called the “invariant special relativity” (ISR). In the ISR it is considered that in the four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between the 4D geometric, coordinate-free quantities. It is mathematically proved that in the ISR the electric and magnetic fields are properly defined vectors on the 4D spacetime. According to the first proof the dimension of a vector field is mathematically determined by the dimension of its domain. Since the electric and magnetic fields are defined on the 4D spacetime they are properly defined 4D vectors, the 4D geometric quantities (GQs). As shown in an axiomatic geometric formulation of electromagnetism with only one axiom, the field equation for the bivector field F [33], the primary quantity for the whole electromagnetism is the bivector field F. The electric and magnetic fields 4D vectors E and B are determined in a mathematically correct way in terms of F and the 4D velocity vector v of the observer who measures E and B fields. Furthermore, the proofs are presented that under the mathematically correct Lorentz transformations, which are first derived by Minkowski and reinvented and generalized in terms of 4D GQs, e.g., in [23], the electric field 4D vector transforms as any other 4D vector transforms, i.e., again to the electric field 4D vector; there is no mixing with the magnetic field 4D vector B, as in the usual transformations (UT) of the 3D fields. Different derivations of these UT of the 3D fields are discussed and objected from the ISR viewpoint. The electromagnetic field of a point charge in uniform motion is considered and it is explicitly shown that 1) the primary quantity is the bivector F and 2) that the observer dependent 4D vectors E and B correctly describe both the electric and magnetic fields for all relatively moving inertial observers and for all bases chosen by them. This formulation with the 4D GQs is in a true agreement, independent of the chosen inertial reference frame and of the chosen system of coordinates in it, with experiments in electromagnetism, e.g., the motional emf. It is shown that the theory with the 4D fields is always in agreement with the principle of relativity, whereas it is not the case with the usual approach with the 3D quantities and their UT.

Multiple reference frame-based current harmonic control for interior PMSMs considering motional EMF

For permanent magnet synchronous machines (PMSMs), current harmonics need to be controlled under two kinds of conditions. Under the first condition, the current harmonics caused by the non-sinusoidal back-electromotive force (EMF) and the dead time of inverters should be suppressed. Under the second condition, specific current harmonics should be injected to suppress the torque ripple of motors. Therefore, the accurate control of current harmonics is critical. It has been found that the original multiple reference frame (MRF)-based control algorithm cannot effectively achieve the control of current harmonics at high speeds. For the currents in MRFs, motional EMF was dominant rather than induced EMF at higher speeds. As a result, the original MRF-based control algorithm does not work at high speeds. To solve this problem, this paper proposed a novel MRF-based control algorithm that considers motional EMF. Furthermore, this paper achieved decoupling control of the current harmonics in MRFs for interior PMSMs. With the proposed control algorithm, the current harmonics of interior PMSMs can be controlled at both high and low speeds. Under the influence of non-sinusoidal back EMF and the dead time of the inverter, the effect of current harmonic control was verified on a laboratory test bench.

Emf generated by squeezing an ellipse * *Authors contributed equally and are listed alphabetically.

We study the motional emf generated by squeezing an elliptical conducting loop traversed by a constant magnetic field. The circumference of the loop remains constant in the elastic regime, acting as a non-trivial constraint. We numerically find the dependence of one axis of the ellipse on the other and hence calculate the rate of change in area and the ensuing emf. We discuss possible applications of our findings.

Mathematical Modeling of a Linear-Induction Motor Based on Detailed Equivalent Circuits

Electric drives based on traction linear-induction motors are used in industry and city transport. The main advantages of this electric drive are unrestricted acceleration and vehicle climbing angles, as well as ecological cleanliness. The development of high-speed design and analysis software tools for linear electric motors is thus becoming quite timely. The use of the finite-element method for solving field problems in a three-dimensional setting and dynamic vehicle-operation regimes is time-consuming. It is proposed to use a detailed magnetic equivalent circuit of a linear-induction-motor longitudinal section with the introduction of the Bolton coefficient to correct for the transverse-edge effect in a solid secondary element. Model features based on multilayer magnetic equivalent circuits are shown, and the effect of the number of layers on the designed motor-traction force is evaluated. When selecting an appropriate pole pitch-to motor gap ratio, a two-level equivalent circuit turns out to be suitable. The secondary element is represented in the model as a set of rectangular rods connected in parallel. The influence of the calculation method of the secondary rods’ motional EMF on the motor-traction-force accuracy is shown. The greatest error is observed in a low-slip region (when the motor passes into a generative braking regime) and the simplest spatial derivative of the magnetic flux. When the derivative calculation formula becomes more complicated, the indicated error sharply decreases. Another way to reduce the calculation error of the motional EMF in the secondary element circuit is to increase the number of these circuits by decreasing the width of the elementary rod. The prominence of the detailed magnetic equivalent-circuit method and convenience of online viewing should be noted.

The Motional EMF in Conductors with Ferromagnetic Shield

The motional EMF in segments of the copper wire with magnetic shielding is found according to the voltage lack in two coils with partial shielding moving relative to the magnetic field lines. The first coil moved across the Earth’s magnetic field lines. The second one was located near the end face of the rotating disk magnet with an axial magnetization. Permalloy foil wound around a part of turns containing wire was used for shielding. The experiments result reveals the penetrating ability of the magnetic field through the ferromagnetic shield and shows the physical nature of the superposition principle. With this in mind, a universal method for calculating EMF induced in a conductive body has been provided as well as the concepts of magnetic field lines velocity and acceleration have been introduced.

In defense of derivations,

At the 2015 AAPT Summer Meeting, I presented four derivations of the formula for motional emf. Such physics derivations involve the construction of explanatory frameworks involving diagrams and mathematical models. Although textbooks devote considerable space to such explanations, many teachers and students spend their time on worksheets, end-of-chapter problems, and the like. The book is reduced to a bank of solved (i.e., example) and unsolved (i.e., homework) questions, along with equations in colored boxes that presumably are to be used to answer those questions. Such an approach encourages fragmentation of knowledge, the view that there is only one right answer to a problem with the goal of physics being to find that answer (neatly boxed of course), and the inability to reason about even a slightly different (much less a novel) situation. If we are to develop scientific literacy, significant course time must be devoted to explaining the structure of and support for the models and equations we use.

Stabilization of magnet assemblies of permanent magnet sodium flowmeters used in fast breeder reactors

Permanent magnet flow meters (PMFMs) are used to measure the sodium flow in sodium cooled Fast Breeder Reactor Circuits. Prototype fast breeder reactor (PFBR) which is under construction at Kalpakkam is a 500MWe, sodium cooled, pool type reactor. Sodium flow measurement in various loops of the reactor is of prime importance from operational and safety point of view. To measure the flow of electrically conducting liquid sodium, in primary and secondary circuit pipe lines of PFBR, permanent magnet flow meters are used. PMFM is a non-invasive device, which works on the principle of generation of motional EMF by magnetic forces exerted on the charges in a moving conductor. Flowmeters of different pipe sizes ranging from 10mm to 200mm pipe diameter are required for PFBR. Long term performance of the flowmeters mainly depends on stability of permanent magnets used in flowmeters to generate constant magnetic field in stainless steel (SS) pipes. This paper describes the effects of time and temperature on permanent magnet assemblies made of ALNICO-V used in PFBR flowmeters. The stabilization methodology for ALNICO-V permanent magnet assemblies is evolved and established. Loss of magnetic field strength with respect to time and temperatures is determined by experiments and found negligible.

Finite difference time domain algorithm for electromagnetic problems involving material movement

The finite difference time domain (FDTD) method, adapted for magnetic field diffusion problems, is used to study the electromagnetic induction in moving materials by including motional emf in standard FDTD electromagnetic equations. The material movement is implemented by continuously changing material properties in each computational cell consistent to material advection. The flux corrected transport (FCT) algorithm is used to transport magnetic field in a fixed eulerian cell. A higher time-step is achieved by artificially increasing permittivity of the medium. This new approach is validated with standard analytical solutions for planar magnetic flux compression system and magnetic field diffusion in moving conductors with a non-relativistic velocity. To our knowledge, this is the first approach to use FDTD method for electromagnetic problems involving material motion.

On the role of induced fields in railguns

We provide a comprehensive analysis of the nature of emfs that are induced during the operation of a railgun. The main sources of these emfs are changes in rail currents and the motion of the armature. Our experience with the current railgun literature and private communications indicates that the topic of induced emfs is a neglected area of analysis.Common misconceptions are discussed and new perspectives are presented. It is shown, for example, that there is a wide diversity of conflicting views on the nature of the emf generated by armature motion. We conclude that there is no true motional emf in railguns, and offer a resolution of the conflicting views in terms of localized flux creation.Finite element modelling is used to illustrate the main concepts and consequences of induced emfs, and to validate the analyses. Experimental data from laboratory railgun tests provide added validation. The results offer insights into many previously unexplained phenomena commonly observed in railguns.

Convection electric field observations near the Arecibo HF heater beam

Electric fields have been observed at the westward edge of the Arecibo HF heater beam, at the F region reflection altitude, by a sounding rocket. We first show that the floating double probe used for these measurements is functioning reliably. The data are shown to be free of sheath rectification effects within the heated volume. Away from the heater beam the double probe data show primarily motional emf, consistent with Earth frame fields of less than 2 m V m−1 (typical, on average, of summer post‐midnight conditions over Arecibo), while near the heater beam, significant Earth frame fields are observed. The convective drift due to these fields is consistent with the apparent drift of simultaneously measured heater‐induced field‐aligned irregularities. The measured convection electric field magnitude is used to estimate the strength of the current maintaining it against the background conductivity, yielding 5 mA m−1. Estimates of the current due to ponderomotive force are lower than this value, unless one invokes electrostatic waves with electric fields roughly 8 times that of the pump field. Temperature gradient currents are estimated as well and are a possible source. The observed shear in the convection electric field is used to estimate a field‐aligned current density of 0.5 μA m−2. We conclude that the heater is indeed driving convection on the scale size of the heated volume but are unable to definitively determine how the corresponding electric fields are being produced.

Current‐induced magnetic field effects on bare tether current collection: A parametric study

The physical process of current collection by a “bare wire” electrodynamic tether in space is considered. The study uses an improved model that takes into account the resistance of the wire and the magnetic shielding induced by current flow in the tether. The plasma density, ne, electron temperature, Te, tether length, L, tether radius, rw and the angle of the geomagnetic field to the tether (90°‐α) were all used as parameters. It is shown, for certain tether configurations and parameter values, that magnetic shielding reduces the collected current. In general, any parametric change that increases tether current, and hence, the strength of the current‐induced magnetic field relative to the strength of the electric field between the tether and the ambient plasma, will increase the shielding effect. Tether current is increased directly with tether collection area (which depends on L and rw), plasma conductivity (which depends on ne and Te), and the motional emf along the tether (which increases with L and the angle 90°‐α). It turns out that, as any of these parameters change so as to cause the overall tether current to increase, the overestimate of current that results from ignoring the magnetic shielding effect becomes correspondingly greater. Moreover, it is shown that a tether system in the thruster (or motor) mode suffers greater current reduction from magnetic shielding than does the same tether deployed in the generator mode. Finally, it is shown that, for certain tether system configurations combined with particular values of the governing plasma parameters, current‐induced magnetic shielding can significantly reduce the collected current and, therefore, system efficiency. For example, in the case of an electrodynamic tether system in the thruster mode under conditions of ne=1.67×106 cm−3, α=60°, rw=2.5 mm, and Em=34 V/km, magnetic shielding will reduce the collected current 10% at a point L=0.65 km along the tether (4.3 A instead of 4.8 A) and this increases to more than 40% at L= 1.3km (9.6 A instead of 13.4A).

Motional EMF demonstration experiment

A simple quantitative motional emf experiment. The induced voltage is recorded in this computer-based experiment as a coil is moved through the field of a permanent magnet. Results compare closely with predicted values.

THEORETICAL COMPARISON OF MOTIONAL AND TRANSFORMER EMF DEVICE DAMPING EFFICIENCY

In this paper, theoretical comparison between electromagnetic dampers based on a “motional emf” and “transformer emf” design is presented. Transformer emf devices are based on the generation of emf in a stationary circuit, in which the emf is generated by a time-varying magnetic field linking the circuit. Motional emf devices are based on the generation of emf due to a moving conductor within a stationary magnetic field. Both of these designs can be used as damping elements for applications such as semi-active and regenerative vehicle suspension systems. The findings herein are provided so as to evaluate the most efficient device for such applications. The analysis consists of comparing the damping coefficient of the electromagnetic devices for a given magnetic field and given volume of conducting material. It has been found that for a limited range of dimensions, the transformer emf devices can be more then 1·2 times as efficient as the motional emf devices. However, for most realistic situations, motional emf devices will have the highest efficiency.

Contactless linear position transducer based on reluctance variation

A novel form of electromagnetic transducer for continuous position sensing in linear drive systems is described. The transducer relies on a repetitive variation of inductance with position caused by the change of reluctance between moving and static saliences of a magnetic circuit. The novelty feature of the transducer is seen in terms of its design which is distinguished by a simple cylindrical modular form and allows a large sensing range. The transducer's accuracy and sensitivity are independent of the sensing range. The investigations presented are focused on studying the magnetic circuit design and the excitation of the transducer, with the aim to accomplish a linear relationship between the transducer output and position. A consideration of the effects of core losses and motional EMF on the transducer output has been made. Results obtained with an experimental prototype transducer are included.

Dwight-Bewley paradox

The concept of motional induced EMF is implicitly based on a reference frame relative to which the magnetic field pattern is unchanging or stationary, and uses the relative v between the frame and the conductor in the expression B v l. For ease of conception, the may be taken as that between the field pattern itself and the conductor. Where there are multiple field patterns in relative motion, no velocity can be ascribed to the resultant field pattern relative to any object, fixed or moving. Therefore the EMF induced in a conductor situated in such a field cannot be expressed as a single motional EMF, but must be found by superposition of EMFs induced by the individual fluxes. From the impossibility of applying the B v l rule to the resultant flux, Bewley concludes that the EMF in the conductor is not motional but variational. It is shown here, mathematically from a consideration of reference frames, and physically from the fact of electromechanical energy conversion taking place, that Bewley's assertion is invalid and that the EMF is in fact motional, not variational. The B v l rule is then generalised for application to such situations.

Some pedagogical aspects of motional EMF

The traditional pedagogy with which motional EMF is introduced to undergraduates is re-examined and a more careful analysis of the work done on charges in a simple model system is presented.

Observations of plasma wave turbulence generated around large ionospheric spacecraft: Effects of motionally induced EMF and of electron beam emission

We report on observations of plasma wave turbulence generated during electron beam injections, spacecraft potential variations, and neutral gas emissions of the CHARGE 2 sounding rocket experiment. The payload was flown in a mother/daughter configuration, with the two sub‐payloads electrically connected by an insulated, conducting tether. While tethered, the two platforms were separated, drifting apart in a direction perpendicular to both the magnetic field and to the spacecraft velocity, reaching a maximum distance of 426 m at the end of the flight. The mother carried a high‐voltage (HV) system (0–460 V), biasing the mother negative relative to the daughter. The operation of the HV bias system simulated the motional emf induced in larger orbiting space structures like the Tethered Satellite System 1 (TSS 1) space shuttle mission scheduled for the spring of 1992. In addition, the mother carried an electron beam accelerator (1 keV, 0–46 mA). The daughter diagnostics included wave receivers (400 Hz to 10 MHz) connected to a pair of electric dipole antennas. Broadband ELF/VLF turbulence was generated both during electron beam emissions and when the HV bias system was operated, while turbulence in the HF range was observed only during electron beam emissions. As a result of the electrical connection through the tether, the ELF/VLF wave intensities show little variation with separation distance of the two payloads. Two sources of wave turbulence are proposed to account for the observations: (1) wave turbulence generated by the beam/spacecraft system in particular in the HF range, and (2) electron return currents to the daughter stimulating VLF noise during HV operations and electron beam emissions.

Comparison of two techniques for closed-loop drive of VR step motors without direct rotor position sensing

Closed-loop control of variable-reluctance (VR) step motors without using direct rotor-position sensing is investigated. Two nondirect rotor-position sensing techniques, namely the waveform detection (WD) and the pulse-width-modulation (PWM) techniques, were implemented and applied to a four-phase (15 degrees step-angle) VR step motor. Test results show that a DC shunt motor and a DC series motor type of performance can be achieved from the step motor with PWM drive and WD drive, respectively. The stability problem encountered with the existing PWM controller due to motional EMF effects at higher operating speeds is investigated, and modifications are suggested to include speed as an additional control signal to make the system more stable. With the inclusion of the speed signal, the operating speed of the test motor is from 1000 to 1750 r/min. The performances for the two techniques are compared, and experimental results are presented. >

Application of special relativity to a simple system in which a motional emf exists

The currents that result from a motional emf in a simple circuit are considered. The speed of the moving parts of the circuit need not be small in comparison to the speed of light. Four simple examples are considered. In each example, the induced emf determined from Faraday’s law is used to calculate a current, which is identified with conduction current. For some observers, the conduction current does not have the same value in all parts of the simple circuit considered here. In parts of the circuit, the total current may include convection current as well as conduction current. The effects of self-inductance are neglected.

Io's wobbling flux tube and nonuniform surface conductivity: Longitude control of decametric emission and other magnetospheric interactions

A model is proposed relating Io's modulation of Jupiter's decametric radio emission (DAM) and other magnetospheric interactions to periodic changes in flux tube orientation with Io’s surface of nonuniform surface electrical conductivity. Spectral reflectance and albedo data suggest that visually bright surface areas on Io may be highly conducting due to the abundance there of irradiation‐altered salts, while relatively dark areas may be extremely insulating due to the abundance of free sulfur. Geometric correlations show that Io's orbital motion through Jupiter's tilted and offset magnetic field results in a 13‐hour periodic variation in the Io‐graphic surface position of Io's flux tube contact junctions. The resulting variation in effective electrical conductivity of Io results in modulation (switching) of Io's motional emf currents and corresponding flux tube currents. This causes the observed magnetic‐longitude dependence of Io‐dependent DAM, while emission beaming accounts for the observed Io‐phase effect. This switching model suggests that Io is a variable unipolar inductor and that its flux tube varies in electrodynamic character as a function of magnetic longitude; the predicted behavior is consistent with pre‐Voyager observed particle‐injection spikes at Io's L shell, auroral emissions from Jupiter, and may reconcile inconsistencies between theoretical and observed particle sweeping effects of Io. The model predicts a relatively inactive flux tube current system and strong particle sweeping during the Voyager 1 flux tube crossing.