Effective Magnetic Permeability Research Articles

Analysis of microwave heating of copper powder compacts

The influence of the native oxide films, which is essential for the understanding of the microwave heating of metal powder, is analyzed numerically based on the experimental data on temperature, dilatation and resistance of compacted copper powder samples. The indicative thickness of the oxide films, determined from the resistivity data using an effective medium approximation, is shown to decrease from ≥1 μm to below 1 nm. The effective complex dielectric permittivity and magnetic permeability of the copper powder with oxide films on the particles are calculated within the recently developed models. The dielectric permittivity exhibits a percolation behavior in the temperature range of the oxide decomposition, viz. 210–250 °C when microwave heating is carried out in nitrogen and 330–375 °C – in argon. The efficiency of absorption of the incident 30 GHz microwave radiation in a slab of powder is assessed separately for the electric and magnetic-type losses, the contribution of the latter being predominant until the percolation transition. The energy flux density of the incident microwave radiation required to sustain the prescribed heating rate is shown to increase during the microwave heating process from ∼20 W/cm2 to >1 kW/cm2 due to increasing reflection. The additional microwave energy input required for the completion of the endothermic oxide decomposition reaction is shown to be significant at the initial stage of the process (below 200 °C).

Influence of Magnetic Polarization on Diagrams of Inductive and Electromagnetic Logs

Abstract ––We present the results of the study of the effect of induced magnetic polarization of clay beds under the influence of an external harmonic electromagnetic field (frequencies 70 and 875 kHz). A two-stage numerical modeling procedure is proposed. At the first stage we determine the effective relative magnetic permeability of a synthetic sample with inclusions of clay particles. In this case a 3D heterogeneous mesh sample is generated. Then we numerically model a spatial distribution of an electric field. The electromotive force (EMF) induced in the measuring coil is calculated from this distribution. Relative magnetic permeability is determined by comparison with EMF of homogeneous samples with different values of magnetic permeability. It has been found that during the electric field excitation by an alternating current coil, the effect of induced magnetic polarization appears in the sample with clay particles. Its manifestation is that the effective magnetic permeability becomes complex. At the second stage we calculate the EMF diagram of the three-coil logging probe in the macro-model ‘clay cap – reservoir’. Magnetic permeability of the clay cap is given by a complex value. In the generated logs, extremes appear in the vicinity of the bottom of the clay cap; they do not correspond to the distribution of electrical conductivity and magnetic permeability in the given model. They can be incorrectly interpreted when analyzing real logs into individual formations. Numerical modeling at all stages is performed by the Vector Finite Element Method on a consistent adaptive tetrahedral partition and the first-order Webb vector basis.

The Effect of Magnetically Induced Local Structure and Volume Fraction on the Electromagnetic Properties of Elastomer Samples with Ferrofluid Droplet Inserts

The magnetic permeability (μ), dielectric permittivity (ε) and electrical conductivity (σ) of six elastomer samples obtained by mixing silicone rubber (RTV-530) with a kerosene-based ferrofluid in different volume fractions (φ), 1.31%, 2.59% and 3.84%, were determined using complex impedance measurements over a frequency range of 500 Hz–2 MHz. Three samples (A0, B0 and C0) were manufactured in the absence of a magnetic field, and the other three samples (Ah, Bh and Ch) were manufactured in the presence of a magnetic field, H = 43 kA/m. The component μ″ of the complex effective magnetic permeability of all samples presents a maximum at a frequency, fmax, that moves to higher values by increasing φ, with this maximum being attributed to Brownian relaxation processes. The conductivity spectrum, σ (f), of all samples follows the Jonscher universal law, which allows for both the determination of the static conductivity, σDC, and the barrier energy of the electrical conduction process, Wm. For the same φ, Wm is lower, and σDC is higher in the samples Ah, Bh and Ch than in the samples A0, B0 and C0. The performed study is useful in manufacturing elastomers with predetermined properties and for possible applications such as magneto-dielectric flexible electronic devices, which can be controlled by the volume fraction of particles or by an external magnetic field.

Аналитический расчет значения магнитной проницаемости суспензии магнитных частиц в немагнитной жидкости

The issues of the hyperthermia method is primarily associated with attempts to concentrate the electromagnetic field, which has a heating effect, in the area of influence using an introduced suspension of magnetic nanoparticles. These particles are concentrated using a magnetic field in the desired area and then heated by an alternating electromagnetic field, thereby heating the body tissue to provide a therapeutic effect. To determine the heating temperature and its connection with the parameters of the acting electromagnetic field, it is necessary to know the electromagnetic parameters of the heated medium, namely the body tissues and the introduced suspension of magnetic particles. First of all, it is necessary to determine such suspension parameters as effective magnetic permeability and effective conductivity. This work is devoted to the analytical solution of the problem of determining the effective magnetic permeability of a suspension of magnetic particles in a liquid.

Microstructure and properties of FeSiCr/Al2O3/epoxy resin soft magnetic composites with high flowability by dry milling and coupling modification

FeSiCr/Al2O3 modified powders were prepared by dry milling and coupling for different durations, and FeSiCr/Al2O3 epoxy resin composites were prepared by banburying and low-pressure molding. The melt index, bending strength, magnetic permeability, and magnetic loss of the FeSiCr/Al2O3 epoxy resin composites were measured. The microstructures of the different FeSiCr/Al2O3 modified powders and FeSiCr/Al2O3 epoxy resin composites were observed using scanning electron microscopy (SEM), and their effects on the flowability, magnetic, and mechanical properties of the composites are discussed. The results showed that dry milling and coupling modification greatly improved the flowability of the FeSiCr/Al2O3/epoxy resin composites. Moreover, the bending strength and effective magnetic permeability increased, and the core loss decreased. Based on the loss data, a new loss separation method that is different from the conventional low-frequency method is proposed. Residual, hysteresis, and eddy current loss were in descending order in the frequency range of 100–2000 kHz.

Time‐harmonic field‐circuit model for brushless doubly fed induction machine

AbstractA computationally efficient time‐harmonic finite element model for the steady‐state analysis of a brushless doubly fed induction machine (BDFIM) is proposed. In the model, the electromagnetic couplings of the BDFIM are described by means of the sum of two complex magnetic vector potentials that represent the two fundamental harmonic time components of the magnetic flux density distribution in the rotor frame of reference. As in an ordinary induction motor, the non‐linearity of the magnetisation characteristic is accounted for using an effective magnetic permeability. For the BDFIM, this is derived by considering the features of modulated magnetic flux density waveform. The accuracy of the approach has been validated by comparing the characteristics of a D270 machine operating in the double‐feed mode with ones obtained from the experimentally verified time‐stepping model at various operating conditions. High accuracy of the results coming from the proposed model is demonstrated even under deep saturation conditions within the magnetic circuit.

EFFICIENCY ENHANCEMENT OF PHOTOVOLTAIC SOLAR CELLS USING METAMATERIALS ABSORBING SCREEN

This paper proposes a novel technique for the efficiency enhancement of photovoltaic (PV) solar cells using metamaterials absorbing screens. This kind of engineered material comprises resonant metallic rings that are printed on a host low-loss dielectric substance and made periodic in a two-dimensional lattice. The absorbing screen has been carefully designed, and its retrieved effective constitutive parameters, effective electric permittivity ϵeff and effective magnetic permeability µeff, are integrated within a numerically modelled amorphous-Silicon-based PV solar cell structure as an impedance matching layer. Such arrangement will greatly achieve matching between the effective impedance of the composite solar cell structure and free-space impedance and will result in higher photons absorption through the metamaterials anti-reflective screen. Numerical full-wave electromagnetic simulations are carried out using CST Microwave Studio for the design of a metamaterial absorbing screen. Due to the large computational resources required, COMSOL Multiphysics was adopted in the design and analysis of the composite structure comprising a two-dimensional PV solar cells layer. Based on the numerical results, both optical and electric characteristics of the PV solar cell structure were enhanced with the use of a metamaterial layer. Moreover, efficiency enhancement by 5% was permissible, in which efficiency reached 12% with the use of metamaterials as compared to the efficiency of the classical PV cells of 7%. The obtained results are very promising, and the potential integration of metamaterials in commercial PV solar cells will show significant advancement in efficiency enhancement of PV cells and realization of smart PV solar cells with the consideration of additional features from metamaterials.

Asymptotic homogenization in the determination of effective intrinsic magnetic properties of composites

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.

The Microwave Absorption in Composites with Finemet Alloy Particles and Carbon Nanotubes.

The absorption of waves of the centimeter and millimeter wavebands in composites with Finemet alloy particles and carbon nanotubes has been studied. It has been established that ferromagnetic resonance and antiresonance are observed in such composites. A method is proposed for calculating the effective dynamic magnetic permeability of a composite containing both a random distribution of ferromagnetic particles and a part of the particles oriented in the same way. In the approximation of effective parameters, the dependences of the transmission and reflection coefficients of microwaves are calculated. It is shown that the theoretical calculation confirms the existence of resonant features of these dependences caused by ferromagnetic resonance and antiresonance. The theory based on the introduction of effective parameters satisfactorily describes the course of the field dependence of the coefficients and the presence of resonance features in these dependences. The frequency dependence of the complex permittivity of the composite is determined. The dependence of the complex magnetic permeability on the magnetic field for millimeter-wave frequencies is calculated.

Effect of Mixed Acid Fluid on the Pore Structure of High Rank Coal and Acid Fluid Optimization.

Acidizing technology is an important means to increase production in oil-gas reservoirs. In recent years, acidizing technology has been widely used to increase the permeability of coal seams to enhance gas extraction, where acidizing fluid is the key factor to determine the permeability improvement effect by acidizing technology. In order to clarify the influence of mixed acid fluid on the pore structure of high rank coal and seek the optimal mixed acid fluid suitable for acidizing and permeability improvement of high rank coal in the Jiaozuo coal mine area. Taking the Jiulishan Mine in the Jiaozuo mining area as an example, low field nuclear magnetic resonance (LFNMR) test and static dissolution test were conducted to obtain the T2 spectrum, porosity, movable fluid saturation, pore throat distribution, nuclear magnetic permeability, and dissolution rate of coal samples before and after treatment with distilled water and three mixed acid fluids. On this basis, the influence of mixed acid fluid on the pore structure of high rank coal was analyzed and the optimal mixed acid fluid suitable for high rank coal was selected. The results showed that the pore size, number, and volume of all kinds of pore sizes of coal samples treated with distilled water all decreased, which was manifested by the decrease of effective porosity and nuclear magnetic permeability. After acidification, the proportion of micropore volume in coal decreased significantly, the number and proportion of pore volume of mesopores and macropore-microfractures increased significantly, and the connectivity between mesopores and macropore-microfractures was enhanced, which was characterized by the increase in effective porosity and nuclear magnetic permeability of coal samples. After acidification, the pore-throat ratio of adsorption pores of all coal samples decreased, while the pore-throat ratio of seepage pores increased. By comparatively analyzing the change law of pore structure of coal samples before and after acidizing with three kinds of mixed acid fluids, the optimal mixed acid fluid suitable for acidizing and permeability improvement of high rank coal in the Jiaozuo coal mine area was selected, which was 12%HCL +3%HF.

The effect of surface plasmonic resonances on magneto-plasmonic spherical core-shell nanocomposites

In this study, the effect of plasmon resonance on magneto-plasmonic spherical core-shell nanocomposite enclosed in a dielectric host medium is theoretically investigated by applying electrostatic approximation (esa) and Maxwell-Garnet effective medium theories to obtain magneto-optical parameters such as; effective electric permittivity and magnetic permeability as well as the corresponding extinction cross-sections. Likewise, for a fixed size of QDs (of radius nm) numerical analysis was performed to determine the plasmonic resonance effect by varying the parameters such as the metal fraction (β) and the dielectrics (εh) of the host medium on the magneto-plasmonic nanostructures (nss). The results depict that graphs of absorption, scattering, and extinction cross-sections as a function of wavelength have two positions of resonance peaks. The first set of peaks are in the ultraviolet (uv) and the second located in visible regions. These peaks originated from the strong coupling between a regular periodic vibrations of surface plasmons of silver (Ag) with the excitonic state of the dielectric/semiconductor at the internal ( ) and external (Ag/host) interfaces. As β increases, the absorption and scattering cross-sections are blue-shifted in the first peak and red shifted the second set of peaks. Similarly, as εh increases or as β decreases, the sets of resonance peaks for extinction cross-section gets enhanced; while keeping one of these parametric quantities fixed at once. The resulting surface plasmon resonance effect might be utilized in a variety of applications that combines both the plasmonic and magnetic core-shell nanostructures ranging from UV to Visible spectral regions.

Investigation of glass forming ability, crystallization behavior, and soft magnetic properties of Fe–B–P–C–Cu alloy ribbons

The effect of Cu content on GFA, crystallization behavior, and soft magnetic properties in high P Fe84+xB6P6C3Cu1−x (x = 0, 0.2, 0.4, 0.6, and 1.0 at. %) alloy ribbons were systematically investigated to balance the relationship between glass forming ability (GFA), heat treatment window, and soft magnetic properties of high saturation magnetic flux density (Bs) Fe-based nanocrystalline alloys. It was discovered that lowering Cu promotes the formation of an amorphous structure. The GFA of alloys rises from 23 μm for Fe84B6P6C3Cu1 to 29 μm for Fe84.4B6P6C3Cu0.6. Analysis of thermal physical properties shows that when Cu content is between 1.0 at. % and 0.6 at. %, reducing Cu in the alloys does not affect the onset temperature of the first crystallization peak (Tx1), the second one (Tx2), and ΔT (ΔT = Tx2 − Tx1), whereas when Cu content is less than 0.6 at. %, reducing Cu leads to an increase in Tx1 and a decrease in Tx2 and ΔT, which is not conducive to obtaining a wide temperature range of precipitation of a single α-Fe phase. The alloys have a wide range of crystallization annealing temperature (693–753 K) and annealing time (60–6 min) to obtain a low coercivity (Hc) of about 8.0 A/m, high Bs of about 1.80 T, and high effective magnetic permeability (μe) of about 10000 when Cu is between 1.0 at. % and 0.6 at. %. The Bs, Hc, and μe of Fe84.4B6P6C3Cu0.6 alloy annealed at 723 K for 30 min are 1.82 T, 8.1 A/m, and 10820, respectively.

Design and Characterization of Wideband Terahertz Metamaterial Stop-Band Filter.

We propose and design a metamaterial broadband stop-band filter with a steep cut-off in the terahertz region. The filter is based on the flexible structure of metal-dielectric-metal-dielectric-metal (MDMDM). Simulation results show that the filter has a center frequency of 1.08 THz, the square ratio reaches 0.95, and the −20 dB bandwidth reaches 1.07 THz. In addition, it has excellent flat-top characteristics with an average transmission rate in the resistive band of no more than 5%. The relative bandwidth has been up to 99%, and stopband absorption rate has reached more than 98%. The effects of the main structural parameters on the transmission characteristics are discussed. The role of each layer of metal in the filter is explored by studying the effect of the variation of the number of metal layers on the filter. The symmetry of the structure ensures the polarization insensitivity of the filter at normal incidence. The correctness of the simulation results was verified by analyzing the effective permittivity and magnetic permeability. To investigate the transmission characteristics of the metamaterial filter in-depth, we analyzed the electric field strength and surface current distribution at the center frequency of the filter. The designed terahertz filter may have potential applications in terahertz communications, sensors, and emerging terahertz technologies.

The epsilon-mu-near-zero (EMNZ) device realized by a novel structure of air gap ring at microwave frequency

The epsilon-and-mu-near-zero (EMNZ) medium, as a kind of zero-refractive-index material, has broad application perspectives. In general, there are three main methods to realize the EMNZ phenomenon based on conventional metamaterials such as fishnet metamaterials, Dirac-like cone-based metamaterials, and doped ENZ mediums in the full frequency range. However, the above EMNZ metamaterials have complex structures and stringent process requirements, and the development of mature engineering applications outside the laboratory is still a long way off. Herein, a novel, simple and stable air gap ring compatible with the EMNZ medium based on the doping method has been proposed to mitigate the above constraints. The proposed structure is composed of a set of nested metal boxes and an air gap ring formed between the nested metal boxes. By changing the size of the cross-sectional area of the perfect electric conductor (PEC) doped into an ENZ medium to manipulate the air gap ring in the nested metal boxes, the effective magnetic permeability of the whole structure can be adjusted. Finally, the equivalent EMNZ medium characterized by a simple structure can be realized in the microwave band. Thus, the proposed novel air gap ring device exhibits promising potential for broad applications such as frequency selection, impedance regulation, super-coupling, and power splitting.

ЗНИЖЕННЯ РІВНЯ МАГНІТНОГО ПОЛЯ ПІДЗЕМНОЇ КАБЕЛЬНОЇ ЛІНІЇ НА ВІДПОВІДАЛЬНИХ ДІЛЯНКАХ ЗА ДОПОМОГОЮ КОМПОЗИЦІЙНИХ МАГНІТНИХ ЕКРАНІВ КІНЦЕВОЇ ДОВЖИНИ

In the article, the numerical calculation and analysis of three-dimensional magnetic field of underground power cable line with finite-length magnetic shields used to reduce the level of this field on the ground are carried out. Both fill-up soil and filling soil containing magnetic particles and then having effective magnetic properties (=1÷1000) are proposed to used as magnetic shields. The shielding efficiency is studied for underground 330 kV cable line depending on the dimensions and effective magnetic permeability () of the shields. As shown, the use of filling soil with magnetic properties gives a possibility to reduce the field on the ground five times. This type of shielding is more efficient as compared to magnetic fill-up soil. The computed results reveal the non-monotonic variation of magnetic field on the ground above the soil edge zones. The longitudinal size of these zones is in the order of the depth of the cables. References 16, figures 9.

Tunable beam propagation based on cylindrically symmetric gradient index system

In this work, a cylindrically symmetric gradient-refractivity two-dimensional electromagnetic system is constructed by using the magnetic metamaterials consisting of an array of ferrite rods. With the change of the bias magnetic field, the different gradient-refractivity systems can be obtained, based on which a tunable flexible beam is demonstrated. Based on the effective-medium theory, the effective electric permittivity and the effective magnetic permeability can be retrieved and thus the effective refractive index is obtained straightforwardly. It is shown that with the variation of the ferrite rod radius, an effective refractivity profile with particular gradient can be realized, which exhibits the electromagnetic “black-hole-like” effect. Especially, the gradient refractivity profile is also designed by introducing the gradient bias magnetic field, which, in principle, results in the refractivity profile with many different gradients. Finally, the propagation of a Gaussian beam in the gradient-refractivity system is simulated by using the multiple scattering theory. A few different phenomena are observed such as the “black-hole” effect, the interior beam deflection, the exterior beam deflection, and the beam splitting. Furthermore, the functionalities can be switched between each other by controlling the bias magnetic field and adding an additional degree of freedom for beam propagation.

Effects of phosphorus substitution on amorphous formation, crystallization behavior and magnetic properties of FeSiBCuNb alloys

Fe-Si-B-Cu-Nb nanocrystalline alloys exhibit excellent soft magnetic properties and have been increasingly applied in high frequencies ranging from several kHz to several hundred kHz, but the magnetic permeability needs further to design to meet the magnetic components under different frequencies. In the present work, the influences of phosphorus substitution on amorphous forming, crystallization behavior and soft magnetic properties of silicon-rich Fe-Si-B-Cu-Nb alloys were systematically investigated. It was found that the suitable addition of 1 at.% of P in Fe-Si-B-Cu-Nb alloy can significantly improve the amorphous forming ability, reduce the coercivity (Hc) of the annealed alloys and elevate the effective magnetic permeability (μe) at frequencies ranging from 1 to 30 kHz in spite of having fractional detriment to the alloy's thermal stability but still remaining a relatively broad annealing temperature region. Besides, the μe in high P-containing alloys becomes insensitive to frequencies at high frequencies region, which can attain frequencies-dependent constant magnetic permeability induced by composition design.

Enhancement of the optical response of Fe3O4@Ag core-shell nanoparticles

In this work, the optical properties of Fe3O4@Ag core/shell spherical nanostructures embedded in a dielectric host matrix are investigated theoretically. The theoretical analysis is carried out based on the electrostatic approximation and Maxwell-Garnet effective medium theory to obtain the effective electric permittivity and magnetic permeability, as well as the corresponding refractive index and absorbance. Moreover, for a fixed size of NPs (of radius r2=30nm) numerical analysis is carried out to see the effect of varying the metal fraction (the volume fraction of the metallic shell) (β), the filling fraction (the volume fraction of inclusions in the composite) (f), and the permittivity (εh) of the host matrix on the optical properties of the nanostructures. The results show that graphs of real and imaginary parts of polarizability, refractive index and absorbance as a function of wavelength possess two sets of resonance peaks in the UV and visible regions. These sets of peaks arise due to the strong coupling/interactions of the surface plasmon oscillations of silver with the semiconductor/dielectric at the inner (Fe3O4/Ag) and outer (Ag/host) interfaces and/or to near-field inter-particle interaction. Moreover, the two set of resonance peaks are found to be enhanced with an increase of β,f, or εh; keeping two of these parameters constant at a time. The results obtained can be used in applications that are designed to integrate plasmonic effects of noble metals with magnetic semiconductors in a core/shell nanostructure.

Simultaneous improvements of effective magnetic permeability, core losses and temperature characteristics of Fe-Si soft magnetic composites induced by annealing treatment

In this paper, silicone-resin coating Fe-Si soft magnetic composites (SMCs) with high magnetic permeability, low core losses and good temperature/frequency stability were successfully fabricated. Microstructural characterizations suggest that the thin, continuous and heat-resistant silicone-resin coatings are constructed surrounding magnetic particles. The effective permeability of SMCs is significantly improved to 139.7 and 153.6 when the stress relief annealing temperatures increase to 700 °C and 800 °C, and meanwhile their core losses are obviously reduced to 657 mW/cm³ and 632 mW/cm³ (0.1 T/50 kHz), respectively. Loss-separation analyses confirm that hysteresis losses predominate in the total core losses within quite wide frequency ranges that depend on annealing temperatures, and higher temperature annealing can more effectively decrease hysteresis losses due to larger residual stress relaxation, which contributes to the simultaneous improvements of permeability and core losses. However, for the SMCs annealed at 800 °C, due to partially decomposed silicone-resin coatings, the strong eddy-current effects at high frequency region will cause sharply increased core losses and slightly decreased frequency stability of permeability. Noticeably, the temperature-dependent behaviors of core losses and permeability of Fe-Si SMCs can be also effectively tuned by optimizing annealing treatment.

Improving Sensitivity and Resolution of Planar Magnetic Inductive Sensors by Optimizing Gap Between Magnetic Films

The sensitivity and resolution of the planar magnetic inductive sensors are enhanced by optimizing the gap between the upper and lower magnetic films. The tradeoff between the effect of the effective magnetic permeability and magnetic leakage of the magnetic films on the inductance of the sensor produces a gap that optimizes the sensor performance. This conclusion is verified theoretically and experimentally with the fabrication and testing of planar magnetic inductive sensors with given dimensions of magnetic films and planar spiral coil. From the analysis, the optimal gap ( g) for our manufactured sensors with given dimensions is four times the magnetic film thickness ( t). Experimentally, when g/t=4, the inductance value, inductance ratio, and voltage sensitivity of sensors are all the largest. The sensitivity and resolution of the sensor with g/t=4 are 1.81 mV/Oe and 50.23 nT at 500 kHz. Compared with the prototype whose magnetic films and planar coil are stacked tightly together, the sensitivity is increased by 43.72% and the resolution is improved by 33.51%. It is universally applicable that there is a gap that optimizes the performance of the planar magnetic inductive sensor.