Biot-Savart Research Articles

THE THEOREM ON THE MAGNETIC FIELD OF ROTATING CHARGED BODIES

The method of retarded potentials is used to derive the Biot-Savart law, taking into account the correction that describes the chaotic motion of charged particles in rectilinear currents. Then this method is used for circular currents and the following theorem is proved: The magnetic field on the rotation axis of an axisymmetric charged body or charge distribution has only one component directed along the rotation axis, and the magnetic field is expressed through the surface integral, which does not require integration over the azimuthal angle . In the general case, for arbitrary charge distribution and for any location of the rotation axis, the magnetic field is expressed through the volume integral, in which the integrand does not depend on the angle . The obtained simple formulas in cylindrical and spherical coordinates allow us to quickly find the external and central magnetic field of rotating bodies on the rotation axis.

Electric and Magnetic Field Estimation Under Overhead Transmission Lines Using Artificial Neural Networks

In this paper, a novel method for electric field intensity and magnetic flux density estimation in the vicinity of the high voltage overhead transmission lines is proposed. The proposed method is based on two fully connected feed-forward neural networks to independently estimate electric field intensity and magnetic flux density. The artificial neural networks are trained using the scaled conjugate gradient algorithm. Training datasets corresponds to different overhead transmission line configurations that are generated using an algorithm that is especially developed for this purpose. The target values for the electric field intensity and magnetic flux density datasets are calculated using the charge simulation method and Biot-Savart law based method, respectively. This data is generated for fixed applied voltage and current intensity values. In instances when the applied voltage and current intensity values differ from those used in the artificial neural network training, the electric field intensity and magnetic flux density results are appropriately scaled. In order to verify the validity of the proposed method, a comparative analysis of the proposed method with the charge simulation method for electric field intensity calculation and Biot-Savart law-based method for magnetic flux density calculation is presented. Furthermore, the results of the proposed method are compared to measurement results obtained in the vicinity of two 400 kV transmission lines. The performance analysis results showed that proposed method can produce accurate electric field intensity and magnetic flux density estimation results for different overhead transmission line configurations.

Investigating the Axonal Magnetic Fields Corresponding to Delta and Theta Waves in the Human Brain Using Direct Detection MRI

This study showed an alternative and non-invasive method for measuring brainwaves using Magnetic Resonance Imaging (MRI) with a gradient echo - echo planar imaging (GE-EPI) sequence. An attempt was made to measure the axonal magnetic fields of delta and theta waves using direct detection with MRI. Time-varying brainwaves produce an axonal current which may induce a magnetic field according to the Biot-Savart law. The MR scanner can detect inhomogeneous magnetic fields caused by weak currents generated in a subject that interact with the main magnetic field, $B_{o}$ , of the scanner. Fifteen healthy volunteers were scanned with closed eyes in a dark imaging room. The GE-EPI sequence was used to acquire 1500 time frame images in an axial plane on a 3.0 T Philips scanner. A Butterworth bandstop filter was applied to filter out physiological signals before the detection of brainwave signals. Fast Fourier Transform (FFT) was used to produce frequency spectra where the brainwave frequencies could be detected. Our study measured an axonal magnetic field of 1.5 ± 0.2 nT for the delta waves and 1.5 ± 0.3 nT for the theta waves. Delta waves were found in the range 1.5–4.0 Hz and theta waves in the range 4.0–6.5 Hz. The waves were found on both sides of the occipital lobe, temporal lobe, and hippocampus. We detected more theta waves (2.1% of the brain slice with 5 mm thickness) than delta waves (1.5% of the brain slice with 5 mm thickness). PLCC for the % $\vert \Delta S/S_{eq}\vert $ between the delta and theta waves was 0.7584 at $p =0.001$ significance level and 95% confidence level. We also applied Short Time Fourier Transform (STFT) with epoch lengths of 3.85 s, 7.7 s, and 30.8 s. But the appearance of brainwave signals was not as clear as using FFT over the entire imaging duration.

Design of a dedicated circular coil for Magnetic Resonance Spectroscopy studies in small phantoms and animal acquisition with a 3 Tesla Magnetic Resonance clinical scanner

Abstract Introduction: Magnetic Resonance Spectroscopy (MRS) is a very powerful tool to explore the tissue components, by allowing a selective identification of molecules and molecular distribution mapping. Due to intrinsic Signal-to-Noise Ratio limitations (SNR), MRS in small phantoms and animals with a clinical scanner requires the design and development of dedicated radiofrequency (RF) coils, a task of fundamental importance. In this article, the authors describe the simulation, design, and application of a 1H transmit/receive circular coil suitable for MRS studies in small phantoms and small animal models with a clinical 3T scanner. In particular, the circular coil could be an improvement in animal experiments for tumor studies in which the lesions are localized in specific areas. Material and methods: The magnetic field pattern was calculated using the Biot–Savart law and the inductance was evaluated with analytical calculations. Finally, the coil sensitivity was measured with the perturbing sphere method. Successively, a prototype of the coil was built and tested on the workbench and by the acquisition of MRS data. Results: In this work, we demonstrate the design trade-offs for successfully developing a dedicated coil for MRS experiments in small phantoms and animals with a clinical scanner. The coil designed in the study offers the potential for obtaining MRS data with a high SNR and good spectral resolution. Conclusions: The paper provides details of the design, modelling, and construction of a dedicated circular coil, which represents a low cost and easy to build answer for MRS experiments in small samples with a clinical scanner.

Development of a biaxial grid-coil-type electromagnetic acoustic transducer

This study proposes a grid-coil-type transducer to achieve the simultaneous detection of axial and circumferential cracks in the pipeline, reduce the number of permanent magnets in dynamic detection, and improve crack detection efficiency. The proposed system can detect biaxial cracks in the pipeline. Based on Biot–Savart’s Law, a mathematical model is established between the magnetic induction intensity and the coil of the electromagnetic acoustic transducer to determine the influence on the conductor. Experiments verify the relationship between the guided wave propagation characteristics of the grid-coil-type electromagnetic acoustic transducer and the ability to detect biaxial cracks. Results show that the grid-coil-type electromagnetic acoustic transducer can generate the biaxial ultrasonic guided wave propagating along the axial and circumferential pipeline, in which cracks are thereby simultaneously detected. Thus, the grid-coil-type electromagnetic acoustic transducer increases the detection scope, reduces the number of permanent magnets in dynamic detection, and improves crack detection efficiency. This study provides a theoretical and experimental basis for the research and engineering application of biaxial crack detection in the pipeline.

Localization and Actuation for MNPs Based on Magnetic Field-Free Point: Feasibility of Movable Electromagnetic Actuations.

Targeted drug delivery (TDD) based on magnetic nanoparticles (MNPs) and external magnetic actuation is a promising drug delivery technology compared to conventional treatments usually utilized in cancer therapy. However, the implementation of a TDD system at a clinical site based on considerations for the actual size of the human body requires a simplified structure capable of both external actuation and localization. To address these requirements, we propose a novel approach to localize drug carriers containing MNPs by manipulating the field-free point (FFP) mechanism in the principal magnetic field. To this end, we devise a versatile electromagnetic actuation (EMA) system for FFP generation based on four coils affixed to a movable frame. By the Biot–Savart law, the FFP can be manipulated by appropriately controlling the gradient field strength at the target area using the EMA system. Further, weighted-norm solutions are utilized to correct the positions of FFP to improve the accuracy of FFP displacement in the region of interest (ROI). As MNPs, ferrofluid is used to experiment with 2D and 3D localizations in a blocked phantom placed in the designed ROI. The resultant root mean square error of the localizations is observed to be approximately 1.4 mm in the 2D case and 1.6 mm in the 3D case. Further, the proposed movable EMA is verified to be capable of simultaneously scanning multiple points as well as the actuation and imaging of MNPs. Based on the success of the experiments in this study, further research is intended to be conducted in scale-up system development to design precise TDD systems at clinical sites.

Biot-Savart law in quantum matter

We study the topological nature of a class of lattice systems whose Bloch vector can be expressed as the difference of two independent periodic vector functions (knots) in an auxiliary space. We show exactly that each loop as a degeneracy line generates a $\mathbf{P}$ field, which is defined as the gradient of the Zak phase in parameter space, obeying the Biot-Savart law: The degeneracy line acts as a current-carrying wire, while the $\mathbf{P}$ field corresponds to the generated magnetic field. Applying the Amp\`ere's circuital law on a nontrivial topological system, we find that two Bloch knots entangle with each other, forming a link with the linking number being the value of Chern number of the energy band. In addition, two lattice models, an extended Qi-Wu-Zhang (QWZ) model and a quasi-one-dimensional model with magnetic flux, are proposed to exemplify the application of our approach. In the aid of the Biot-Savart law, the pumping charge as a dynamic measure of Chern number is obtained numerically from quasi-adiabatic processes.

A novel exact analytical expression for the magnetic field of a solenoid

In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible thickness with a stationary electric current. We derive the expressions of the on- and off-axes magnetic field components. The results have been compared to some simplified and known analytical formulae as well as to a commercial numerical code showing a good agreement.

Optimization and Testing of a 1H/3He Double-Nuclear Quadrature Transmit Coil, Applying the Analytical Method at 0.06T

Application of polarized noble gas technology in lung functional magnetic resonance imaging (fMRI) has garnered attention for its unique advantages, such as high resolution and a lack of radiation exposure. This paper presents a 4-channel radio frequency (RF) coil design method for applications of an 1H/3He MRI system at the ultra-low field of 0.06T. For the complex model of the double-nuclear 1H/3He coil, the analytical optimization method (based on the theories of Biot-Savart law and PSO algorithm) and the electromagnetic (EM) field and radio frequency (RF) circuit co-simulation method was implemented to optimize the analysis, resulting in an effective evaluation. The simulation results demonstrated that the proposed model has the potential for imaging of the lung with the 1H/3He MRI system at an ultra-low field.

The role of the “monopole” instability in the evolution of two-dimensional turbulent free shear layers

The role of instability in the growth of a two-dimensional, temporally evolving, “turbulent” free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot–Savart relation. The initial evolution of perturbations in a constant vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman–Rubach–Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan, Narasimha, and Hari Dass [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)] and a universal value of the ratio of dominant spacing of structures (Λf) to the layer thickness (δω). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing “base” flow. The model of Morris, Giridharan, and Lilley [“On the turbulent mixing of compressible free shear layers,” Proc. R. Soc. London, Ser. A 431, 219–243 (1990)], which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of Λf/δω achieved in the universal self-preserving state.

Efficient Reduction of Powerline Signals in Magnetic Data Acquired From a Moving Platform

High-bandwidth magnetic data are normally distorted by ubiquitous 50- or 60-Hz noise from powerlines and similar sources. The powerline noise can be orders of magnitude larger than the magnetic signal from targets and must be culled from data sets prior to interpretation. Suppression of the powerline noise by simple filtering can result in artifacts and an unacceptable reduction in resolution of ground-based and unmanned aerial vehicle magnetic surveys. Removal approaches such as those based on Biot–Savart modeling are sensitive to the estimated position of the powerline systems, in addition to their limited applicability due to the requirement of a DC source. Moreover, the powerline noise in data acquired from a moving platform is inherently nonstationary and removal techniques must be specifically developed with this in mind. We propose a model-based method that does not rely on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the powerline system by fitting and subtracting a set of sinusoids to the data. These sinusoids are computed on small windows of data, tied together with regularization terms within the fitting process to reduce discontinuities between segments. We further incorporate powerline frequency as a nonlinear parameter, allowing for fluctuations in the fundamental frequency as loads on the power grid change. Through synthetic and field examples, we show that periodic noise can be reliably removed automatically without the need for filtering or significant alterations of the frequency content. Powerline noise is reduced by over 98% in the field example.

Inhibition of B16F10 Cancer Cell Growth by Exposure to the Square Wave with 7.83+/-0.3Hz Involves L- and T-Type Calcium Channels

ABSTRACT Extremely low-frequency electromagnetic field (ELF-EMF) exposure influences many biological systems; these effects are mainly related to the intensity, duration, frequency, and pattern of the ELF-EMF. In this study, exposure to square wave with 7.83±0.3 Hz (sweep step 0.1 Hz) was shown to inhibit the growth of B16F10 melanoma tumor cells. In addition, the distribution of the magnetic field was calculated by Biot-Savart Law and plotted using MATLAB. In vitro studies demonstrated a decrease in B16F10 cell proliferation and an increase of Ca2+ influx after 48 h of exposure to the square wave. Ca2+ influx was also partially blocked by inhibition of voltage-gated L- and T-type Ca2+ channels. The data confirmed that the specific time-varying ELF-EMF had an anti-proliferation effect on B16F10 cells and that the inhibition is related to Ca2+ and voltage-gated L- and T-type Ca2+ channels.

Reconstruction of Current Density Distribution in Low-Voltage Switching Devices Through TSVD and TGSVD Regularization

This article examined two regularization methods for reconstructing the arc current density distribution of a switching device in an arc-quenching chamber. The finite-element method (FEM) was used to discretize the current-flow region of the arc-quenching chamber. Both truncated generalized singular value decomposition (TGSVD) and truncated singular value decomposition (TSVD) regularization were used to reconstruct the current density distribution. TGSVD addressed the poor reconstruction accuracy caused by the ill-posedness of the Biot–Savart operator. Simulation results showed that the reconstruction of current density distribution was more accurate with higher signal-to-noise ratios (SNRs) and lower mean-square errors (MSEs). Both regularization methods were accurate with low noise levels, although the reconstruction accuracy of TGSVD was more sensitive to noise than that of TSVD regularization.

A high precision in-bore velocity measurement system of railgun based on improved Bi-LSTM network

The B-dot magnetic probe array is one of the most common method to measure the in-bore velocity of electromagnetic railgun projectile, but in the exiting research, the errors caused by armature shape and the uneven distribution of current are often ignored. In order to achieve more accurate velocity measurement, this paper calculates probes induced voltage based on the Biot–Savart theorem for the projectile with C-shaped armature. Based on the analytic expression of evaluation, the positions of magnetic probes are corrected by using the cuckoo searching (CS) algorithm. In order to solve the problem that the accuracy of velocity measurement system declines under the condition of some abnormal probe signals, this paper proposes an improved Bidirectional Long Short-Term Memory (Bi-LSTM) network with Correction Head Network (CHN), and trains the whole network based on the experimental data which is under the same working condition. The algorithm proposed in this paper is verified by simulation and experiment. The results show that the position correction method of B-dot magnetic probes and the data repair method of damaged probe can effectively improve the accuracy and robustness of the in-bore velocity measurement system.

Multipole Expansion of Radiation From Patch Antenna Using Quasi-Static Surface Currents

In this letter, the multipole expansion of the fields radiated from a rectangular microstrip patch antenna on an infinite ground plane is presented. Such multipole expansion allows calculating the fields at any distance (near and far fields) from the antenna. It is shown that the coefficients of the expansion can be obtained from the quasi-static fields due to the quasi-static currents on the edges of the patch. The static fields are calculated on a spherical surface enclosing the patch and its image in the infinite perfect electric conductor (PEC) ground plane by applying the duals of Coulomb's and Biot–Savart's laws. Using only the radial components of the fields on the enclosing sphere, the multipole coefficients and, hence, the fields outside the sphere are calculated. The field distributions obtained using such multipole expansion match well with the corresponding analytical approximations in the far-field and HFSS simulation results. The spatial evolution of the field components with distance from near field to far field for the patch is presented. The minor deviations of the obtained results from that of simulations and the limitations of the proposed method are discussed.

Optimal Phase Arrangements of Underground Transmission Lines Installed by Metropolitan Electricity Authority of Thailand

This paper investigates the magnetic field generated by underground transmission lines, which are practically installed by Metropolitan Electricity Authority (MEA) of Thailand. Specifically, various phase arrangements for duck bank (4×6) and pipe-jacking (21 ducts) of the MEA underground transmission lines were analyzed and simulated by analytical approach based on Biot-Savart Law using MATLAB program. To assure the accuracy of the simulated results, they were compared to the measured results under the same conditions where the test cite was at the tunnel link between Lad-Phrao and Vibhavadi substations, about 8 km, and the tunnel depth was at 15 m from the ground surface. In addition, the magnetic field was simulated from the measured RMS current, recorded every 30 seconds for 16 hrs. By aforementioned setting conditions, the optimal phase arrangements of MEA underground transmission lines in terms of minimized magnetic field for duck bank (4×6) and pipe-jacking (21 ducts) were proposed. Finally, from the simulated results, it shows that the magnetic field generated by underground transmission lines with proposed optimal phase arrangement techniques is not greater than the maximum exposure limits given by the World Health Organization and International Commission on Non-Ionizing Radiation Protection.

A Design Method for Magnetically Coupled Resonant Coils Considering Transmission Objectives and Dimension Constraints

This paper proposes a coil design method for the magnetically coupled resonant wireless power transfer (MCR-WPT) system. Based on the Biot–Savart law, the magnetic flux density at the observation point was derived, and the magnetic flux of the observation plane generated by the exciting coil was deduced to build the calculation model of power transfer efficiency (PTE) and power delivered to the load (PDL). The PTE and PDL curves via coil parameters could be fitted in minutes using numerical calculation. The coil was designed according to transmission objectives and dimension constraints. In addition, the calculated PTE and PDL were compared with those from finite element analysis to verify the credibility of the method. Finally, the actual curves of PTE and PDL were achieved, which showed a strong positive correlation with the corresponding curves from the calculation model. The relative average deviations of PDL curves were less than 6.11%. Meanwhile, coils designed with the numerical calculation could realize 309.80 W and 88.51%, which achieved the objectives under the constraints. The results demonstrate that the proposed method can realize a rapid and accurate coil design under constraints. It can also be applied to other coil structures or circuit topologies with strong universality.

Magnetic field and radiation characteristics of plasma induced by hypervelocity impact on aluminum alloy

Plasma will be formed during hypervelocity impact and accompanied by electromagnetic radiation ranging from low frequency to high frequency. It is a significant physical phenomenon under strong impact loadings and the main cause of electromagnetic damage suffered by spacecraft. This paper focused on the aluminum alloy and established the model of the magnetic field based on the movement of the plasma and the Biot-Savart law. The magnitude and microwave radiation characteristics of the induced magnetic field under different collision velocities and target thicknesses were analyzed. It is found that the magnetic field generated by the plasma expansion has a high frequency in a form of pulsed oscillation. The maximum magnetic induction intensity, the power spectral density of electronic oscillation and the total energy of microwave radiation are positively correlated with the collision velocity. The thinner the target is, the greater the magnetic induction intensity, the shorter the duration of the strong pulse and the smaller the power spectral density and the total energy of the microwave radiation will be.

On the Edge Singularity of the Actuator Disk Model

AbstractIn this technical brief, the classic actuator disk theory is revisited with a view to shed some light on the singularity of the flow at the edge of the disk where the vortex tube starts and where vorticity is generated. The study is carried out using small perturbation assumption in two-dimensions and simplified boundary conditions in all cases. The problem of the two-dimensional thin cambered plate with constant vorticity distribution is solved and the leading edge singularity is analyzed as it is believed to be relevant to the axisymmetric flow at the actuator disk edge. Next, the velocity components induced by the cylindrical vortex tube of constant vorticity are obtained via the Biot–Savart law and the near edge behavior is investigated. It is shown that the velocity components behavior is consistent with that of the thin cambered plate with constant loading, thus reinforcing the notion that the axisymmetric slip-line behaves as r − R ∝ −xlnx near the disk edge.

Feasibility analysis of a modular uniform magnetic field coil.

In this paper, a feasibility analysis of a modular uniform magnetic field coil is provided. The modular uniform magnetic field coil consists of n2 square coil units. By adjusting the number of coil units or the current in the coil units, different sizes and patterns of uniform magnetic field coils can be easily formed to meet different experimental requirements. An analytical model of the modular uniform magnetic field coil considering the gap between coil units is first developed based on the Biot-Savart law and the superposition principle, and the analytical model is verified by the 3D finite element method. Then, the characteristics of the modular uniform magnetic field coil are analyzed and compared with the traditional Helmholtz coil, demonstrating the advantages of the proposed magnetic field coil. These advantages precisely verify the original intention of the modular uniform magnetic field coil proposed in this paper. Finally, a robustness analysis of the modular magnetic field coil is performed, including the effects of gap between coil units and assembly misalignment on the performance of the modular uniform magnetic field coil.