Field-free **magnetic** **vector** **potential** . In classical electrodynamics, the magnet- ic field of **induction** B is determined [10] by equation B = curl A , where A is a **magnetic** **vector** **potential**. In shielding of **magnetic** field, B = 0 , the following may take place: A ≠ 0 . This case is referred to as the field-free **vector** **potential**. **Magnetic** **vector** **potential** has a physical meaning of its own. In 1949, Erenberg and Siday predicted the ability of **magnetic** **vector** **potential** to influence directly the characteristics of quantum entities even though there is no electromagnetic field at the location of the entities [11]. In 1959, the possibility of such an effect was considered by Aharonov and Bohm [12]. Subsequently, a great number of experiments have been conducted which confirmed the theoretical predictions [13]. In general, these experiments were as follows (see Figure 2): the beam of electrically charged quantum entities emitted by a source is split into two beams:

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Figure 3(a),(b),(c) and (d) respectively show the **Magnetic** **Vector** **Potential** (A) plot in Wb/m, **Magnetic** Flux Density Contour Plot in Tesla, torque and speed profile of 2/6 pole BDFIM when only the SPW is excited. A clear flux linkage pattern can be observed around 6 poles of the machine and the **magnetic** flex density is coming within the limits with reference to Table 4 [5]. The torque curve under no load condition consists of ripples in the waveform oscillating around the base zero reference since it is on no load and which is then shifted to full load condition with 25 Nm at 0.56 seconds. For 6 pole mode, the synchronous speed is 1000 rpm as given in equation 2. From the results, it is proved that the machine runs in **induction** mode of operation with a value of speed below the synchronous speed and when got loaded to 25 Nm, the speed of machine decreased to 780 rpm.

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That is to say , since the magnetic field in this hypothetical experiment has absolutely no "physical" contact with the sensing wire, we must conclude that the el[r]

With the advent of **magnetic** gears, researchers have developed a new breed of permanent-magnet machines. These **magnetic**- geared permanent-magnet machines artfully incorporate the concept of **magnetic** gearing into the permanent-magnet machines, leading to achieve low-speed high-torque direct-drive operation.Gears and gearboxes are extensively used for speed change and torque transmission in various industrial applications. It is well known that the mechanical gear has a high torque density, but suffers from some inherent problems such as contact friction, noise, heat, vibration and reliability are of great concern. In order to avoid these types of problems we are using **magnetic** meshing gears. That is the gears are meshed together with the help of **magnetic** force of attraction without making into contact. By using such kind of gearing systems we can reduce the wear and tear that are commonly seen in mechanical spur gear systems and the **magnetic** gears works smoothly without any sound and the main advantage of **magnetic** gearing is it will not get heated as long as it works. **Magnetic** gearing systems can be used in vehicle transmissions that reduce the friction and improve the efficiency without using any type of additional lubricants. We are using high power rare earth neodymium magnets for the purpose of making gears. Neodymium magnets are powerful magnets which are about 12 times stronger than normal magnets used in speakers.

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Subsequent tempering produced a simulated service entry microstructure, i.e. tempered martensite/bainite as shown in Fig. 1 (b) with the majority of the laths measuring around 380 7 149 nm wide (consistent with previous data [20]) as measured from SEM images. Some areas without clear lath features are present in the SEM images (probably due to non-uniformity in etching) and were not considered in the measurement. Compared to the as-normal- ised P9, there is a signi ﬁ cant decrease in the number density of low angle boundaries as observed from Fig. 2(b) and (d) due to coarsening of the martensitic laths. Many ﬁ ne alloy carbides are present along the lath boundaries, together with some coarse equiaxed precipitates. The size of the latter is inconsistent with their formation during tempering and so they are more likely to be coarse carbides from the service-exposed condition that failed to dissolve completely and remained from the prior solution heat treatment as shown in Fig. 1(b). However, these carbides are so widely separated that they are expected to have a negligible effect on the overall pinning of DW motion, compared to other ﬁ ne precipitates. Although reverse **magnetic** domains can form around them, there are too few for these precipitates to have a signi ﬁ cant effect on the EM properties.

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In recent time there is increase in demand of **Induction** Motor in industries. In this paper we present the sensorless method for speed estimation and control of three phase **induction** motor . No sensors are used so this system isrugged and simple. The dynamic model of the **induction** motor is derived by using a two-phase motor in direct and quadrature axis.

• When the magnetic flux can be expressed in When the magnetic flux can be expressed in terms of the line integral of vector potential,. terms of the line integral of vector potential,[r]

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In the past few years, MIT has been primarily developed for medical imaging applications such as imaging brain function or stroke detection [6]. Previous MIT mainly used fixed coils array, and all coils are located around the periphery of the imaging area. Each coil of the system is both of a sensor coil and a drive coil [7– 10]. The MIT systems achieve circumference measurement by switching the func- tions of coils. The continuous monitoring function of MIT has an advantage in the treatment of traumatic brain injury, however, the brain surgical operations and the wound care unable to supply suitable space for the typical MIT system. It means that the sensors need to give way to the treatment and care in the place of the wound (i.e. the coils cannot take operating area). The system cannot achieve the monitoring of the brain without a complete sensor array in these cases. In the limited-angle MIT imaging study, a part of the coil array (these coils have exciting and detection func- tions) has been directly abandoned. The incomplete measurement images cannot be used as a diagnostic basis. So, the sensor array design needs to achieve complete measurement, and the system can provide enough operating region simultaneously. The distribution of the drive **magnetic** field is a sector in the imaging area. This fea- ture makes the sensor array can locate high-sensitivity region, and the other area set as the operating region. Therefore, the design strategy of sensor distribution is proposed based on the simulation analysis results of edge **magnetic** **induction**. The sensor array locates on the space where the **magnetic** field has high information effectiveness.

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Abstract. Electrostatic charging has long been used to improve the efficiency of a range of sprayed liquids. However, the benefits have not until recently been available for exploitation by domestic sprays due to the need for a high voltage power supply. A minimum charge-to-mass ratio (q/m) of 1 × 10 -4 C/kg is generally considered necessary to elicit electrostatic benefits. This level of charge can now be imparted to liquids atomised from trigger-actuated spray devices by a passive system, requiring no power supply. **Induction** charging was achieved using a triboelectrically charged aluminium electrode. The q/m of the sprayed liquid was dependent upon the charge residing on the **induction** electrode. The **induction** electrode was electrically isolated and required a charge of between 0.7 and 1.3 × 10 -8 C to deliver a water spray with a q/m of 1 × 10 -4 C/kg. This level of static charge was readily attained by tribocharging the aluminium with polythene. Once generated, sufficient charge remained on the electrode surface to charge successive sprays without the need for regeneration. The performance advantages for a spray charged in this manner include attraction to and targeting of surfaces and wrap-around onto surfaces not in the direct line of sight.

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For the two photons of **vector** **potential** A and − A , their rotation angle frequency ω , and motor direction are same, they can condense into photon- couple, it is shown in Figure 6. With Equation (23), we can find the two photons should be in the balance state, since they suffer the electromagnetic attraction and the spin repulsion. The photon-couple total **vector** **potential**, total electric field **magnetic** field, total spin and momentum all are zero, and the two photons energy should be absolutely transformed into mass of photon-couple, it is

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The paper deals with the analysis of 4-coil Active **Magnetic** Bearing system by the Finite Element Method and the **magnetic** **vector** **potential** formulation. This work proposes an optimal shape and dimensions of the rotor and air gap. This paper also presents how the FEM Analysis can be used to perform the **magnetic** field analysis in the Active **Magnetic** Bearing (AMB). This paper reports ANSYS simulation of 4-coil AMB that uses four attraction type magnets are placed in 900 apart from each other. The AMB is an integral part of the industrial rotational machine laboratory model. The nonlinear solution of the **magnetic** **vector** **potential** is determined by using the 2-D finite element method. The force is calculated by Maxwell’s stress tensor method. The electromagnetic field distribution and density analysis allow verifying the designed AMB and the influence of the shaft and coil current changes on the bearing parameters.

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• Comparisons of our elliptic integral formulas with Refs. [19, 21, 27]. The zonal harmonic **magnetic** field calculation method has several important advantages. First, the field and source equations are separated: during the source constant computations one has to use only the source point and source parameters (geometry, currents, magnetization), but not the field point parameters; and during the field computation the source constants contain already the whole information about the **magnetic** sources. As an important consequence, the **magnetic** field calculation with the zonal harmonic method is much faster (in some cases even 1000 times) than with the widely known elliptic integral method. Second, the zonal harmonic method has not only high speed, but also high accuracy, which makes the method especially appropriate for trajectory calculations of charged particles. Due to these properties, no interpolation is necessary when the **magnetic** field during particle trajectories is computed with the aid of the zonal harmonic method. Third, it is more general and for practical applications more advantageous than the radial series expansion method, which is more widely known in the electron optics literature than the zonal harmonic method. In addition, the zonal harmonic field series formulas are relatively easy to differentiate and integrate, in contrast to the elliptic integral formulas. Furthermore, the low-order source constants can be helpful for system design optimization; for example, vanishing low-order central source constants imply a homogenous **magnetic** field near the central source point.

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Abstract—This paper presents an exact analytical method to compute the air-gap **magnetic** ﬁeld of surface-mounted permanent-magnet (SMPM) motors for evaluating slotting eﬀects accurately. Solution ﬁeld regions are divided into air-gap domain, permanent magnets (PM) domain, and slot domains. The Laplace’s equations or Poisson’s equations of the sub-domains are contacted by boundary conditions and then solved by exact analytical method. The actual height of slot and distance between slots are taken into account in the computation. **Magnetic** ﬁeld distributions and cogging torque computed with the proposed analytical method are compared with those issued from 2-D ﬁnite-element method (FEM), and the comparison results are consistent and show the correctness and eﬀectiveness of the proposed analytical method.

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∂ ∂ − ∂ ∂ = − enables us to reduce the problem of finding the six components associated with the two vectors E E x E y E z = x ˆ + y ˆ + z ˆ and B B x B y B z = x ˆ + y ˆ + z ˆ down to four components – the scalar **potential** V and the **vector** **potential** A A x A y A z = x ˆ + y ˆ + z ˆ . As we saw last semester in P435, B r t ( ) , = ∇× A r t ( ) , and E r t ( ) , = −∇ V r t ( ) , − ∂ A r t ( ) , ∂ t do not enable us to uniquely define / specify / determine the scalar and **vector** potentials V r t ( ) , and A r t ( ) , ; only **potential** differences V 2 – V 1 and A 2 − A 1 are physically meaningful…

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The research work reported in this paper mainly deals with the preparation by an economical methods and characterizations of some BiFeO 3 , CeFe 2 O 3 -BiFeO 3 nanocomposites and Carbon Nanotubes. Multiferroics are the **potential** keystones in upcoming **magnetic** data storage and spintronics devices provided a simple and fast way can be found to turn their electric and **magnetic** properties on and off. The present experimental study on synthesis and characterizations of xCrFe 2 O 4 -(1-x) BiFeO 3 Multiferroic nanocomposites, with x = 0.0, 0.1, 0.2, 0.3 and 0.4 can be used as reference work and be extended for further studies with different ‘x’ values for different properties. Further, this work can be extended to study the carbon nanotubes may be reinforced into BiFeO 3 nanoceramics and convert to metallically conductive composites. By using spark- plasma-sintering method [89], we can fabricate nanocrystalline BiFeO 3 matrices that retain the integrity of SWCNT in the matrix. The conductivity of these composites increases with increasing content of CNTs.

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performance. However, the study about the air gap **magnetic** ﬁeld, torque and the change mechanism of the loss in damper bars when the generator is running at asymmetrical state is less. The energy conversion between stator and rotor is realized by the air gap **magnetic** ﬁeld. The torque ripple and average torque of generator are respectively related to the stable operation and load capacity. The eddy current loss of the damper bars is the main loss of the generator, which directly determines the eﬃciency of the generator. Therefore, the study about the air gap ﬂux density, torque and eddy current loss is extremely essential.

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Magnetorheological Fluid, called MFR, is an active branch in the research of intelligent material field. MFR is made of tiny soft **magnetic** particles and non-conducting **magnetic** mother liquid with high permeability and low hysteresis of **magnetic** and mixed with an emulsifier[1]. Under the action of external **magnetic** field, MRF can instantly ( in milliseconds ) achieve consecutive reversible transition between the low viscosity easy flow of Newtonian fluid and high viscosity hard plastic Bingham[2]. It has a wide range of applications in many fields because of its "liquid", "solid" state transition reversible, controllable and rapid and other outstanding technological features[3]. In the current technology, Bossis and Cutillas et al from French University of Nice has done a lot of work in the MRF mechanism research, especially in the aspect of microstructure analysis[4]. Kormann et al from Germany BASF G have developed a stable of nanoscale MRF[5]. The engineering and technical personnel Lord company has developed a vehicle seat suspension damper[6]. Gm Foister and Gopalswamy developed magnetorheological Fluid and magnetorheological clutch[7]. Jianhua Ni[8] from Xi’an Jiaotong University had carried out a research on the

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In this section, the presented analytical model is used to study the **magnetic** flux density, electromagnetic torque, back- electromotive force, self-inductance and mutual inductance of four prototype motors. The results of analytical method are then verified by the results of finite element method. A 2D model of the studied brushless permanent magnet motor is shown in Fig. 1 and the motor parameters are given in Table 1. The matrix connection between the stator slots and phase connections of each layer for the investigated motors are given by

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Abstract—Power pads for charging batteries of electric vehicles in the garage have been in existence for many years but they have not solved the problems facing the users. Electric vehicles stop anywhere on the road as soon as the energy stored in the batteries is exhausted. Stationary charging systems are common and usually located at designated charging stations. To overcome the problems associated with the stationary charging system especially in developing countries, we propose the design of power pad for dynamic battery charging system. This model employs wireless power transfer mechanism, utilizing high quality **magnetic** resonance. The work leverages on the ability of energy to be transferred efficiently between two magnetically coupled resonating coils in a complex electromagnetic environment. A prototype of the dynamic battery charging system was designed and constructed.

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