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The basic physics of magnetic fields is presented for a target audience of NMR workers. This group often does not have formal training in electromagnetism, but could benefit from an understanding of a selected subset of topics. The focus here is on a relatively non-mathematical view, intended to deliver an intuitive understanding of the topic. The covered topics start with the fields arising from simple idealized currents, including long straight wires, short flat coils, infinite current sheets, long solenoids, and magnetic dipole moments. The generation of field gradients and shim fields is discussed. All of these can be unified by considering the divergence and curl of the magnetic field. Magnetic materials are treated, both linear magnetizable materials (including the sample itself) and permanently magnetized materials; the approaches of equivalent currents and Ampere's theorem for magnetic circuits are presented.

Abstract A new semi‐analytical expression is presented based on two integrations for calculating the magnetic force of a solenoid inductor wound by rectangular cross‐section wire. The authors simplified the solenoid inductor coil to a collection of circular coils, and the current density of the coils in the radial direction which was inversely proportional to its radius is considered. The obtained expressions can be implemented by adaptive Gaussian quadrature integration with MATLAB programming. In addition, they used the filament method and the finite element method to calculate the magnetic force on the solenoid inductor coil. The correctness of the semi‐analytical expressions was verified by comparing the results of the semi‐analytical numerical method with those of the filament method and the finite element method, respectively. The derived semi‐analytical expressions of magnetic force allow a low computational time compared with the filament method and the finite element method to a specific accuracy. The calculation results show that: the solenoid inductor coil tends to compress in the axial direction, and the axial magnetic force on the outermost coils is the largest; the solenoid inductor coil tends to expand outward in the radial direction, and the radial magnetic force on the intermediate coil is the largest.

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

To improve the linearisation of the variable flow-regulate system under the open-loop control, a proportional solenoid valve with high-linearity performance was developed to meet that requirement of the high-precision and open-loop control. The design of the proportional solenoid valve evolves the optimisation of a magnetic circuit structure, the construction of a balanced pressure structure and the compensation of a feedforward control device. As for the solenoid, it is very challenging to meet the requirement of 95% linearity. A feedforward control device with the Bouc–Wen model and a quadratic inverse function model is a good solution to address the hysteresis problem and achieve better performance. The optimisation of a simple magnetic circuit with low sensitivity to the moving armature and a balance chamber for removing the pressure difference are both preconditions to make the compensation. The feedforward control device is the next step to eliminate the hysteresis problem and non-linear characteristics of the solenoid by solving model coefficients measured in the test. After the improvement in these aspects, the proportional solenoid valve can meet the demand of digital proportional flow control with >98% linearity and excellent repeatability, through the validation of both no-load and high-load performance tests.

This study first analyses the problems that the solenoid valve generates during operation. Then the electromagnetic valve was modelled and ANSYS finite element analysis simulation software was used to simulate the electromagnetic field and transient magnetic field of the solenoid valve. The magnetic induction intensity distribution diagram and magnetic field distribution diagram of the electromagnet were obtained. According to the simulation results of the solenoid valve, the magnetic flux leakage line is blocked after the magnetic isolation cover is added, the magnetic induction strength of the iron core and the valve head is increased, the leakage magnetic flux is reduced, and the structure is optimised.

Various controls for fluid flow and pressure are now required in related industries, and the pulse width modulation (PWM) and dithering techniques have become essential for the proportional control of solenoids. However, there is a fatal drawback when the dither current signals are generated as a by-product of low frequency PWM. That is, the average current and the dither amplitude in low frequency PWM cannot be controlled independently. Therefore, a new method for maintaining constant dither amplitudes is proposed in this paper. Throughout the mathematical analysis, the effect of PWM frequency and duty cycle on the average current and dither amplitude was investigated, and the analysis result was validated by electrical experiments. Based on the mathematical analysis, a new method that properly varies both the duty cycle and the PWM frequency to obtain the desired average current and constant dither amplitude was established and verified. This method requires only the calculations for determining the proper PWM frequency and duty cycle, so it is possible to improve the performance of a proportional solenoid valve without additional devices or cost.

Wear is one of the common faults in the mechanical transmission system. Detection of wear particles in lubricating oil can detect and evaluate the wear degree of mechanical equipment. The electromagnetic sensor for metal wear particle detection can be connected in series with the oil circuit, which has the advantages of full liquid flow, simple structure, distinguishing metal properties, and not being influenced by bubbles and vibration. In view of the shortcomings of the existing electromagnetic sensor for wear particle detection, the detection principle and the induction electromotive force model were studied, and the magnetic field change of the metal particles through three coil differential solenoids was analysed. The optimisation design method was proposed here, which was about the related parameters, such as the wire diameter, the coil turns, the coil widths and so on. The experimental analysis of the sensor was carried out based on detection hardware system that could provide the phase-locked amplification function. The 10-mm inner diameter sensor could detect the minimum 100-μm ferromagnetic metal abrasive particles after optimisation. The developed sensor could provide data information for the abrasive particle detection, fault diagnosis and early warning of wear degree of mechanical equipment.

If the magnetic resonance coupling-based wireless power transmission system has multiple receivers, cross-coupling will occur between the transmitter and the receiver, resulting in the variation of transmission characteristics when compared with the case of a single receiver. To solve this problem, a mutual inductance coupling circuit model for double-relay and multi-load transmission system and a calculation model for mutual inductance between solenoid coils in the same plane have been built to study the transmission characteristics of the system through simulation and testing. The study results show that: the cross-coupling effect between the transmitter and the receiver will cause resonance frequency shift, or even lead to the variation of resonance frequency splitting characteristic; when compared with a single-load system, the multi-load system may increase in total transmission power and efficiency; generally, with the introduction of additional receivers, the receiving power and efficiency of the original loads will decrease; along with the increase in circuit spacing and the decrease in cross-coupling, the transmission characteristics will gradually regress to the state of a single-load system. In this article, the calculation model for mutual inductance is correct and the maximum relative error in these calculating examples is 5.28%.

The methods of conductive supracrystalline nanotubes spiralization are shown. Such coiled nanotubes can be used as the solenoids in nanoelectronic components of radio-technical systems. The calculations of conductance of the solenoids and inductance of the magnetic field created into them are given.

In the past few decades, the multifunctional magnetic drug carrier based on the magnetic nanoparticles and high magnetic field has been intensively researched. The magnetic drug carrier can be targeted to the tumour area not only by the chemical protocol but also by the physical one (external field). In this review, the authors first briefly discuss the fabrication process of magnetic drug carriers, which includes the synthesis of magnetic nanoparticles, fabrication of magnetic drug carriers and conjugation of anti-tumour agents. Then different targeted protocols have been summarised, including passive targeting, biochemical active targeting and biophysical active targeting namely magnetic targeting (MT). Multiple MT results both in vitro and in vivo are introduced, in which two unconventional cases are emphasised and described. The first MT clinical research with 14 peoples was performed in the last century. A 0.5–0.8 T permanent magnet was attached to the tumour area when magnetic particles conjugated with epirubicin were injected. The side effect of epirubicin had been decreased, and the four patients showed the decreasing of a tumour which proved the feasibility of MT. Different from other targeting protocols, MT needs an extra external magnetic field. So various types of MT instruments have been shown in the final part of this review, including a single strong magnetic field, homemade electronic solenoid coil assay and commercial magnetic resonance imaging.