Spherical Conductor Research Articles

Fast Recognition on Shallow Groundwater and Anomaly Analysis Using Frequency Selection Sounding Method

The validity of the frequency selection method (FSM) in shallow (<150 m) groundwater exploration was illustrated by practical applications, and the relationship between potential electrode spacing MN and groundwater depth in FSM sounding method was analyzed and preliminary theoretical research was carried out by a simple geologic-geophysical model of sphere. Firstly, under the combined action of horizontal alternating electric field and alternating magnetic field, a simplified geophysical model of low resistivity conductive sphere in homogeneous half space was established, and the forward calculation was performed on the FSM sounding curve. Then, the water yield of 131 wells in the application of FSM in the Rural Drinking Water Safety Project of 12th Five-Year Plan in Guangxi Province was counted. In addition, detailed tabular statistical analysis was carried out on the drilling results of 98 drilling wells, and the relationship between potential electrode spacing MN at abnormal sounding curve and actual drilling water depth was compared and studied. Theoretical analysis and practical application show that FSM has obvious effectiveness in shallow groundwater exploration, and it is an effective method to determine shallow groundwater well locations in the future. The cause of FSM anomaly is the comprehensive effect of the natural 3D alternating electromagnetic signal underground. At the same time, the practical statistics show that there is 1:1 approximation between the size of potential electrode spacing MN at the anomaly curve of the frequency selection method and the actual drilling water depth, which verifies the correctness of the theoretical simulation results. FSM could be widely used in the shallow groundwater exploration in the future, and it is an effective, non-destructive, fast, and low-cost geophysical method.

Mathematical Analysis of Conducting and Dielectric Sphere in Fractional Space

This paper presents an analytical analysis of a sphere placed in fractional dimensional space. The Laplacian Equation in fractional space describes physics as a complex phenomenon. The general solution of the Laplacian equation in fractional space is obtained by the separable variable technique. We have investigated a close form solution for conducting sphere and dielectric sphere. Further, the electric potential and charge density, induced due to a point charge is calculated in fractional space, and also the energy radiated by the sphere is determined. The results are compared with the classical results by setting the fractional parameter α = 3 which normally lies in the limit 2 < α ≤ 3.

Viability of circle and sphere theorems in potential theory and hydrodynamics via Maxwell's conjecture

AbstractIn A Treatise on Electricity and Magnetism, Maxwell determines the angles of intersection for which one may use Kelvin's inversion method to obtain the perturbed electric potential upon placing intersecting spherical conductors into a region with a known potential. There are numerous modern applications utilizing this geometric construction in potential theory and hydrodynamics, and generalized circle and sphere theorems play a foundational role in this area of mathematical physics. In his work, Maxwell gives an intuitive argument for obtaining the perturbed potential based on intersecting planar conductors and a spherical inversion, and in this paper we extend his ideas to a full proof using rotational transformations and reflections. In the process, we disprove results in [Proc Lond Math Soc., 1966:3(16)] and [Stud Appl Math., 2001:106(4); Z. Angew. Math. Mech., 2001:81(8)] on boundary value problems in hydrodynamics involving intersecting circles and spheres, and we detail the angles of intersection for which these theorems are viable. Moreover, our proof recovers a special case overlooked by Maxwell for which Kelvin's inversion method may be utilized to obtain full solutions.

Highly sensitive and selective serotonin (5-HT) electrochemical sensor based on ultrafine Fe3O4 nanoparticles anchored on carbon spheres

Neurotransmitter serotonin (5-HT) is involved in various physiological and pathological processes. Therefore, its highly sensitive and selective detection in human serum is of great significance for early diagnosis of disease. In this work, employing iron phthalocyanine as Fe source, ultrafine Fe3O4 nanoparticles anchored on carbon spheres (Fe3O4/CSs) have been prepared, which exhibits an excellent electrochemical sensing performance toward 5-HT. With carbonecous spheres turned into conductive carbon spheres under the heat treatment in N2 atmosphere, iron phthalocyanine absorbed on their surfaces are simultaneously pyrolysised and oxidized, and finally transformed into ultrafine Fe3O4 nanoparticles. Electrochemical results demonstrate a high sensitivity (5.503 μA μM−1) and a low detection limit (4 nM) toward 5-HT for as-prepared Fe3O4/CSs. In combination with the morphology and physicochemical property of Fe3O4/CSs, the enhanced sensing mechanism toward 5-HT is disscussed. In addition, the developed electrochemical sensor also displays a good sensing stability and an anti-interferent ability. Further applied in real human serum samples, a satisfactory recovery rate is achieved. Promisingly, the developed electrochemical sensor can be employed for the determination of 5-HT in actual samples.

Laguerre–Gaussian Beam Scattering by a Perfect Electromagnetic Conductor (PEMC) Sphere

Laguerre–Gaussian Beam Scattering by a Perfect Electromagnetic Conductor (PEMC) Sphere

Electromagnetic Radiation Force of Vortex Electromagnetic wave exerted on a perfect electromagnetic conductor (PEMC) Sphere

In this manuscript, the electromagnetic (EM) radiation force (RF) exerted on a perfect electromagnetic conductor (PEMC) sphere by a vortex electromagnetic (VEM) wave with spiral phase distribution had been investigated. The analytical formulation of EM fields is being done in the framework of Mie theory, while the field expressions are being modeled considering the features of VEM wave for PEMC sphere. Initially, the incident field coefficients are evaluated using definite integrals. The scattering coefficients are then determined by imposing boundary conditions at the surface of PEMC sphere i.e., at 𝑟=𝑎, leading to a linear system of equations computed via solving matrix. So, a lengthy calculation yields undetermined scattered field coefficients relative to incident field coefficients. The cross-section (𝑄) factors i.e., scattering (𝑄𝑠𝑐𝑎) and extinction (𝑄𝑒𝑥𝑡) have been computed. The influence of sphere size parameter (𝜌) and beam waist radius (𝑤0) versus scattering angle (𝛼°) for the RF along with 𝑄𝑠𝑐𝑎 has been numerically analyzed. As no loss of energy occurs inside PEMC sphere so absorption ((𝑄𝑎𝑏𝑠)=0), by virtue of the energy conservation principle then, 𝑄𝑒𝑥𝑡=𝑄𝑠𝑐𝑎. Under specific condition, we implemented present results on 𝑄𝑠𝑐𝑎 towards light without orbital angular momentum (OAM) i.e., (𝑙=0) and plane wave for the PEMC sphere. The research work has potential applications towards particle manipulation, optical technology, and optical tweezers.

Abstract 3450: Impact of model inaccuracy on dose estimation in TTFields therapy

Abstract Introduction: Tumor Treating Fields (TTFields) is a modality for treating Glioblastoma (GBM). A recent study combining clinical data and simulations demonstrated that the simulation-based dose estimation at the tumor level is directly correlated with patient survival (Ballo M, et al. Int J Radiat Oncol Biol Phys. 2019;104(5):1106-1113). This study highlights the importance of computer-modelling based TTFields treatment planning in the clinic. Performing such planning in a meaningful manner requires an understanding about how inaccuracies in the patient model influence calculated TTFields distributions. In this study we show the effect of local perturbations in the model, errors in tumor segmentation, and inaccuracy in the patient head model on TTFields dose estimation. Methods: Computational studies were performed with Sim4Life software. 1) Local model uncertainty outside of tumor region: To create defects in the models, conductive spheres with varying conductivities and radii were placed into the model’s brains at different distances from the tumor. Virtual transducer arrays were placed on the models, and delivery of TTFields numerically simulated. The error in the electric field induced by the defects as a function of defect conductivity, radius, and distance to tumor was investigated. 2) Tumor segmentation uncertainty: For illustrating segmentation errors in tumors and necrotic cores, layered spheres with various conductivities and radii were placed in different head locations. Tumor conductivity uncertainty was defined as (σ-σref)/σref where σref = 0.24 S/m is the standard tumor conductivity and σ is the varied conductivity over the tumor. The normalized tumor radius was calculated when each of the varied radii was normalized to the results obtained by all the other combinations. Results: The results show that that when a defect of radius R is placed at a distance, d, from the tumor that is larger than seven times R, the error is below 1% regardless of the defect conductivity. Conclusions: Our models and results show the impact of uncertainty in segmentation of the tumor or other tissue distant from it on the TTFields dose estimation. These results could serve as a guideline for model creation and tissue segmentation that would lead to optimal dose estimation in TTFields treatment planning. Citation Format: Tal Marciano, Oshrit Zeevi, Zeev Bomzon. Impact of model inaccuracy on dose estimation in TTFields therapy [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3450.

Vector spherical harmonic analysis and experimental validation of spherical shells illuminated with broadband, millimeter wave Gaussian beams: applications to corneal sensing.

Coupling to longitudinal modes of thin spherical shells, under Gaussian-beam illumination, was explored with a theoretical method based on Fourier-optics analysis and vector spherical harmonics and was scrutinized with an experimental setup. For the theory part, the illumination frequency band was fixed between 100-600 GHz and the outer spherical shell radius of curvature and thickness are 7.5 mm and 0.5 mm, respectively. The shell material was either the lossless cornea or an aqueous effective media representing the cornea. Six different beam-target strategies were introduced being potential candidates for maximum coupling. Two dispersion-tuned beam ensembles with strongly frequency-dependent phase center location have been created with a fixed incident beam 1/e radius and radius of curvature called forward strategies. These computations of different alignments were continued with four beam ensembles of frequency-invariant phase center, constructed from fits to experimental data, oriented at four different axial locations with respect to the spherical shell center of curvature, they are called reverse strategies. Coupling efficiency for all strategies was calculated for different targets including perfect electrical conductor (PEC) sphere, PEC core covered by a cornea loss-free layer and cornea. All scattering strategies contrasted to scattering from equivalent planar targets as a reference with maximum coupling. The results show that, under an ideal calibration, forward strategies are a closer approximation to the plane-wave condition for the cornea. An experimental setup was assembled to explore the simulation approach in a frequency range between 220 GHz to 330 GHz. Two different quartz samples with permittivity of 4.1 were mounted on a water core, acting for a cornea. The first and second quartz radius and thickness were 7.5 mm and 0.5 mm and 8 mm and 1 mm, respectively. An adequate agreement between theory and experiment was confirmed. A particle optimisation swarm algorithm was applied to extract the thickness and permittivity of quartz from the measured back-scattered field for reverse strategies.

Integrated Physical Optics for Calculating Electric-Large Metallic Sphere Scattering Irradiated by Vortex Wave in Microwave Frequency Band

In this letter, a novel integrated physical optics (PO) method for calculating high-frequency scattering of nonplane wave is proposed, and the orbital angular momentum (OAM) wave scattering upon an electric-large metallic sphere is illustrated. A high-order Bessel wave expanded by a series of plane wave angular spectra is selected to irradiate a perfect electric conductor sphere. Combining the PO approximation, the scattered field from the facet element is calculated, and the total scattered effect is obtained by vector superposition of the scattering from all facets. The calculated results are verified by the EM simulated software FEKO and scattering measurement experiment. Numerical results show that the scattered field of the vortex wave passing through the standard target still has the OAM characteristics, retaining the same topological charge. It can be seen that the proposed combined PO method is feasible at high frequency and can be extended to solve the scattering of other beams and objects, which has a broad range of applications.

CuO Nanozymes as Multifunctional Signal Labels for Efficiently Quenching the Photocurrent of ZnO/Au/AgSbS2 Hybrids and Initiating a Strong Fluorescent Signal in a Dual-Mode Microfluidic Sensing Platform.

A novel dual-mode microfluidic sensing platform based on CuO nanozymes as a photoelectrochemical (PEC)-fluorescent (FL) multifunctional signal label was developed for ultrasensitive neuron specific enolase (NSE) detection. Herein, ZnO/Au/AgSbS2 hybrids, possessing excellent PEC properties, were first exploited as a sensing matrix to provide a stable photocurrent. The controlled synthesis of photoactive ZnO nanoflowers (NFs) was successfully conducted using a microfluidic reactor in the scale of seconds. Furthermore, the photocurrent of ZnO NFs decorated by Au and AgSbS2 nanoparticles significantly improved, owing to the local surface plasma resonance effect of Au and matching band structure between ZnO and AgSbS2. A strategy of catalytic oxidation ascorbic acid (AA) by CuO nanozymes was proposed to quench the PEC signals and initiate FL signals. CuO nanoparticles growing on conductive carbon spheres (CuO@CSs) as secondary antibodies' labels could efficiently catalyze the oxidation of AA to achieve a PEC "signal-off" state. Then, the produced dehydroascorbic acid reacting with o-phenylenediamine opportunely generated a strong FL signal. Importantly, wide linear ranges of 0.0001-150 ng/mL for the PEC technique and 0.001-150 ng/mL for the FL method with a low detection limit of 0.028 and 0.25 pg/mL, respectively, could guarantee the sensitive detection of NSE.

Enhancing PFC ability to dye removal and power generation simultaneously via conductive spheres in the anodic chamber

Discharging organic contaminants into the water bodies has become one of the critical problems for the environment. Also, these pollutants are a source of chemical energy. In this study, we introduced a novel photocatalytic fuel cell system with a new design of photoelectrode to treat pollution and produce energy simultaneously. The effect of conductive copper spheres as an electron acceptor to reduce the recombination rate of photogenerated electronsand holes was investigated to improve dye removal, power generation and increase system conductivity. The TiO2/Ti photoanode is designed in a basket for the first time to keep the spheres in the anodic chamber and improve electron transfer through the external circuit. During 5 h, the decolorization of 20 mg/L of methyl orange (MO) reached 86.78%. The short-circuit current, open-circuit voltage, and maximum power density of the PFC were 0.21 mA/cm2, 0.69 V, and 0.033 mW/cm2, respectively. Using conductive spheres improved the system's overall performance by 10%, 23%, and 24%, respectively, compared to when conductive spheres were not used.

A low-cost, portable, two-dimensional bioimpedance distribution estimation system based on the AD5933 impedance converter

This study proposes a low-cost, portable, eight-channel electrical impedance tomograph based on the AD5933 impedance converter. The patterns for current injection and voltage measurement are managed by an Arduino Mega 2560 board and four 74HC4067 Texas Instruments multiplexers. Regarding the experimental results, the errors in the impedance estimates of an electrical circuit that represents a Cole model were less than 1.14% for the magnitude and 4.15% for the phase. Furthermore, the signal-to-noise ratio measured in a resistive phantom was 55.23 dB. Additional experiments consisted of placing five spheres of different size and conductivity in a saline tank, measuring their impedance through eight electrodes, and then generating impedance maps using the Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS). These maps were different for each sphere, suggesting the proposed prototype as a promising alternative for medical applications.

Scattering of arbitrary-shaped optical polarized beams by a PEMC sphere

The generalized Lorenz-Mie theory (GLMT) for a laser beam of arbitrary shape illuminating a perfect electromagnetic conductor (PEMC) sphere is presented. Making use of the vector angular spectrum decomposition method (VASDM), and the multipole expansion method (MEM), in which any beam is expressed in terms of vector spherical wave functions (VSWFs) and beam shape coefficients (BSCs), the BSCs are obtained and expressed by a vector angular spectrum. The incident and scattering waves are expanded using VSWFs. A relation between the coefficients of the scattering fields and the BSCs of the incident beam is established considering the appropriate boundary conditions at the surface of the PEMC sphere. Expressions for the extinction, scattering, and absorption cross-sections are derived and computed. By isolating the co-polarization and cross-polarization components of the scattering coefficients, individual expressions of these physical quantities are also provided. Considering the vector Bessel and Airy polarized beams as examples, the total electric field intensity, scattering cross-section and its co-polarized and cross-polarized components are numerically computed and discussed. The effects of beam polarization, size parameter of the sphere, the admittance M, and beam parameters are analyzed. It has been found that the intensity and distribution of the total (incident + scattered) electric field intensity in the transverse (yz) plane depends on the incident beam characteristics and its polarization states. As the dimensionless size ka increases, the amplitude of the scattering cross-section increases and then decreases as ka increases. As the admittance parameter M changes, there are different characteristics if the incident beam is different. Nonetheless, there is a common behavior that the trend of the co-polarized component of the scattering cross-section decreases first and then increases regardless of the beam and its polarization state. When it comes to the trend of the cross-polarized component versus M, it is opposite to that of the co-polarized component. A few resonance peaks are manifested in the plots when the incident beam is radially or azimuthally polarized. The results may have promising applications in scattering, particle manipulation, optical trapping, and other related researches dealing with a sphere exhibiting rotary polarization.

A Software Package for the Modeling of Electrophysiological Activity Data

A complex of programs has been developed for computer modeling of multichannel time series recorded in various experiments on electromagnetic fields created by the human body. Sets of coordinates and directions of sensors for magnetic encephalographs of several types, electroencephalographs and magnetic cardiographs are used as models of devices. To study the human brain, magnetic resonance tomograms are used as head models; to study the heart, a body model in the form of a half-space with a flat boundary is used. The sources are placed in the model space, for them the direct problem is solved in the physical model corresponding to the device used. For a magnetic encephalograph and an electroencephalograph, an equivalent current dipole model in a spherical conductor is used, for a magnetic cardiograph, an equivalent current dipole model in a flat conductor or a magnetic dipole model is used. For each source, a time dependence is set and a multichannel time series is calculated. Then the time series from all sources are summed and the noise component is added. The program consists of three modules: an input-output module, a calculation module and a visualization module. The input-output module is responsible for loading device models, brain models, and field source parameters. The calculation module is responsible for directly calculating the field and transforming coordinates between the index system and the head system. The visualization module is responsible for the image of the brain model, the position of the field sources, a graphical representation of the amplitude-time dependence of the field sources and the calculated values of the total field. The user interface has been developed. The software package provides: interactive placement of field sources in the head or body space and editing of the amplitude-time dependence; batch loading of a large number of sources; noise modeling; simulation of low-channel planar magnetometers of various orders, specifying the shape of the device, the number of sensors and their parameters. Magnetic and electric fields produced by sources in the brain areas responsible for processing speech stimuli are considered. The resulting multichannel signal can be used to test various data analysis methods and for the experiment planning.

Orbital angular momentum wave scattering from perfect electromagnetic conductor (PEMC) sphere

We studied the orbital angular momentum (OAM) wave scattering by a perfect electromagnetic conductor (PEMC) sphere using Mie Theory. The Vortex Electromagnetic (VEM) wave is well known with a definite amount of OAM. To obtain the OAM wave scattering from PEMC sphere, the conventional plane wave scattering from PEMC sphere expressions are modified by taking into account the characteristics of OAM waves. The unique properties of analytical expression of OAM fields are analyzed, and the scattered field coefficients in terms of incident field coefficients were obtained using boundary conditions. The comparison between conventional scattering for plane wave and OAM wave from PEMC sphere had been carried out. The presented work provides a theoretical insight for the calculation of Radar Cross Section (RCS) by metamaterial as PEMC sphere and identification applications of light carrying OAM in optical manipulation technology.

Enhanced attraction between drops carrying fluctuating charge distributions.

The electrostatic force between conductive spheres is always attractive at small separations, irrespective of their mean charge, when the charge on the spheres is constant. In many situations, the charge may not be fixed, such as for water drops in the natural atmosphere which vary in size and charge. We show that the attractive force between charged conductive spheres increases with increasing charge variance. The importance of this unrecognized electrostatic effect between water drops is evaluated for its potential to enhance rain formation.

MODELING OF A LUNENBURG LENS ANTENNA WITH THE INNER METALIC SPHERE

One of the statutory principle of fifth generation mobile communications is the adaptive antenna system beam-forming technology that allow the radiation to be oriented to specific subscriber. Promising solution of the task can be using the passive antennas, which provide the direct beam-forming with no active component in the circuit, thus is low-cost. Lunenburg lens antenna is perspective solution of the task described above and allows the direct radiation to be formed in wide-angle range and keeps the required performance. Besides, it's slightly compact, so the antenna can be installed on various of city infrastructure elements, and the spherical form of device is advantage when the installation is performed on to the vehicles surface (train, car, aircraft, etc.) In the paper, the metallic sphere installation inside the spherical Lunenburg lens as a mean of attachment to constructions is described. The analysis results of the inner element impact to the antenna characteristics of the Lunenburg lens are provided. Analytical system model with the spherical conductor inside the antenna, which can also be used to calculate the presence of metallic particles impact to the average permittivity of the lens, is shown. The diffraction task is addressed by means of the Green's tensor functions application. The results of numerical modeling of the described antenna system using the Ansys Electronics Desktop (HFSS Design) are presented. Analytical and numerical calculations show that the limited-sized metallic sphere presence inside the lens does not significantly affect the focusing property of the device. The acquired formulas can be used in the future work to find the solution of the metallic element optimal radius approximation, using the neural networks as one of the mean to do it.

An Analytical Method of Electromagnetic Wave Scattering by a Highly Conductive Sphere in a Lossless Medium with Low-Frequency Dipolar Excitation

The current research involves an analytical method of electromagnetic wave scattering by an impenetrable spherical object, which is immerged in an otherwise lossless environment. The highly conducting body is excited by an arbitrarily orientated time-harmonic magnetic dipole that is located at a reasonable remote distance from the sphere and operates at low frequencies for the physical situation under consideration, wherein the wavelength is much bigger than the size of the object. Upon this assumption, the scattering problem is formulated according to expansions of the implicated magnetic and electric fields in terms of positive integer powers of the wave number of the medium, which is linearly associated to the implied frequency. The static Rayleigh zeroth-order case and the initial three dynamic terms provide an excellent approximation for the obtained solution, while terms of higher orders are of minor significance and are neglected, since we work at the low-frequency regime. To this end, Maxwell’s equations reduce to a finite set of interrelated elliptic partial differential equations, each one accompanied by the perfectly electrically conducting boundary conditions on the metal sphere and the necessary limiting behavior as we move towards theoretical infinity, which is in practice very far from the observation domain. The presented analytical technique is based on the introduction of a suitable spherical coordinated system and yields compact fashioned three-dimensional solutions for the scattered components in view of infinite series expansions of spherical harmonic modes. In order to secure the validity and demonstrate the efficiency of this analytical approach, we invoke an example of reducing already known results from the literature to our complete isotropic case.

Impact of Model Inaccuracy on Dose Estimation in TTFields Therapy

<h3>Purpose/Objective(s)</h3> Tumor Treating Fields (TTFields) is a modality for treating Glioblastoma (GBM). A recent study combining clinical data and simulations demonstrated that the simulation-based dose estimation at the tumor level is directly correlated with patient survival (Ballo M, et al. <b>Int J Radiat Oncol Biol Phys</b>. 2019;104(5):1106-1113). This study highlights the importance of computer-modelling based TTFields treatment planning in the clinic. Performing such planning in a meaningful manner requires an understanding about how inaccuracies in the patient model influence calculated TTFields distributions. In this study we show the effect of local perturbations in the model, errors in tumor segmentation, and inaccuracy in the patient head model on TTFields dose estimation. <h3>Materials/Methods</h3> Computational studies were performed with software. 1) Local model uncertainty outside of tumor region: To create defects in the models, conductive spheres with varying conductivities and radii were placed into the model's brains at different distances from the tumor. Virtual transducer arrays were placed on the models, and delivery of TTFields numerically simulated. The error in the electric field induced by the defects as a function of defect conductivity, radius, and distance to tumor was investigated. 2) Tumor segmentation uncertainty: For illustrating segmentation errors in tumors and necrotic cores, layered spheres with various conductivities and radii were placed in different head locations. Tumor conductivity uncertainty was defined as (σ-σ<b>_ref</b>)/σ<b>_ref</b> where σ<b>_ref</b> = 0.24 S/m is the standard tumor conductivity and σ is the varied conductivity over the tumor. The normalized tumor radius was calculated when each of the varied radii was normalized to the results obtained by all the other combinations. <h3>Results</h3> The results show that that when a defect of radius R is placed at a distance, d, from the tumor that is larger than seven times R, the error is below 1% regardless of the defect conductivity. <h3>Conclusion</h3> Our models and results show the impact of uncertainty in segmentation of the tumor or other tissue distant from it on the TTFields dose estimation. These results could serve as a guideline for model creation and tissue segmentation that would lead to optimal dose estimation in TTFields treatment planning.

Dexterous magnetic manipulation of conductive non-magnetic objects

Dexterous magnetic manipulation of ferromagnetic objects is well established, with three to six degrees of freedom possible depending on object geometry1. There are objects for which non-contact dexterous manipulation is desirable that do not contain an appreciable amount of ferromagnetic material but do contain electrically conductive material. Time-varying magnetic fields generate eddy currents in conductive materials2-4, with resulting forces and torques due to the interaction of the eddy currents with the magnetic field. This phenomenon has previously been used to induce drag to reduce the motion of objects as they pass through a static field5-8, or to apply force on an object in a single direction using a dynamic field9-11, but has not been used to perform the type of dexterous manipulation of conductive objects that has been demonstrated with ferromagnetic objects. Here we show that manipulation, with six degrees of freedom, of conductive objects is possible by using multiple rotating magnetic dipole fields. Using dimensional analysis12, combined with multiphysics numerical simulations and experimental verification, we characterize the forces and torques generated on a conductive sphere in a rotating magnetic dipole field. With the resulting model, we perform dexterous manipulation in simulations and physical experiments.