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Concept# Electric displacement field

Summary

In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacitance of a material, as well the response of dielectrics to electric field, and how shapes can change due to electric fields in piezoelectricity or flexoelectricity as well as the creation of voltages and charge transfer due to elastic strains.
In any material, if there is an inversion center then the charge at, for instance, +x and -x are the same. This means that there is no dipole. If an electric field is applied to an insulator, then (for instance) the -ve charges can move slightly towards the +ve side of the field, and the +ve charges in the other direction. This leads to an induced dipole which is described as a polarization. There can be

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In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), is a measure of the electric polarizability of a dielectric. A material

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In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments

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In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, ele

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The topics covered by the course are concepts of fluid mechanics, waves, and electromagnetism.

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Introduction to electromagnetism.

PHYS-201(b): General physics : electromagnetism

Introduction à la mécanique des fluides, à l'électromagnétisme et aux phénomènes ondulatoires

Paul Karoly Otto Ery, Carlotta Guiducci, Kevin Keim, Samuel Kilchenmann, Mohamed Zakarya Alsaid Ali Rashed

This paper reports a method for label-free single-cell biophysical analysis of multiple cells trapped in suspension by electrokinetic forces. Tri-dimensional pillar electrodes arranged along the width of a microfluidic chamber define actuators for single cell trapping and selective release by electrokinetic force. Moreover, a rotation can be induced on the cell in combination with a negative DEP force to retain the cell against the flow. The measurement of the rotation speed of the cell as a function of the electric field frequency define an electrorotation spectrum that allows to study the dielectric properties of the cell. The system presented here shows for the first time the simultaneous electrorotation analysis of multiple single cells in separate micro cages that can be selectively addressed to trap and/or release the cells. Chips with 39 micro-actuators of different interelectrode distance were fabricated to study cells with different sizes. The extracted dielectric properties of HeLa, HEK 293, and human immortalized T lymphocytes cells were found in agreements with previous findings. Moreover, the membrane capacitance of M17 neuroblastoma cells was investigated and found to fall in in the range of 7.49 ± 0.39 mF/m2.

2019Diabete is a disease which is spreading faster than ever, impacting now a larger population. Patients suffering from this disease need the injection of insulin to control extracellular sugar levels. Pharmaceutical companies developed injector pens to allow patients to inject themself the right amount of drug. But the dosage depends on many parameters as the previous meal, current blood sugar level... and a wrong dosage can lead to health problem e.g., loss of conciousness at short terms and severe diseases like cardiac pathologies at long terms... To prevent these situations, a smart pen cap has been developed at Valtronic Technologies to follow and log the individual injections by measuring the level of drug in the pen, the temperature, and the relative humidity to allow the patient and the medical staff to have an history of the injections and the climatic conditions.Injector pen and smart pen cap have been firstly presented with a non-exhaustive list of different physics which can be used to measure a level of liquid. For need of precision, the capacitance technique is the best technology choice. Therefore, the smart pen cap is based on a capacitive sensor. Different capacitance converter topologies have been compared through a bibliographic study. It appears that the Lock-in converter gives the best sensitivity and Charge Sensitivity Amplifier has the lowest power consumption. A trade-of was to use a capacitance-to-digital-converter. A chip from Analog device has been selected due to its high resolution below the femto-farad level, its simple interface and its availability on the market which allows a fast development and industrialisation. Then, switch and electronic structure are presented. First tests with an empty device have been conducted to find the noise floor, which is below 0.1fF.Subsequently, a study of different electrodes configuration has been performed. Firstly, an analysis on two parallel flat electrodes has been conducted using theoretical and simulation approaches. Then, two semi-cylindrical electrodes have been analysed. A comparison has been made between two theoretical methods which are: considering an infinite number of parallel flat electrodes following the shape of the semi-cylindrical electrodes and the conformal mapping methods. This last method gives coherent results when comparing real measurements and simulation. The device is equipped with semi-cylindrical electrodes which allow for a small package and a good correlation between capacitance and drug level with a convertion slope of 0.5fF/µL. Tests have been performed which give an error of +-1 IU and +-4 IU for large injection (set point equal to 72 IU).Finally, the study of some parasitic effects is presented in the last section. An important effect is the climatic effect which affects the capacitance due to variation of electric permittivity linked to temperature change and water absorption of certain materials as plastics. To compensate for this effect, reference electrodes and a climatic sensor have been implemented. Another important effect comes from the cartridge position in the non-uniform electric field of the smart pen cap. A four electrodes device has been realized to allow a perpendicular rotation of the electric field to obtain a more constant averaged electric field. As a consequence, the position impact of the cartridge has been reduced. Other effects have been considered. The device can detect a minimum injection of 52uL.

In this PhD thesis we deal with two mathematical problems arising from quantum mechanics. We consider a spinless non relativistic quantum particle whose configuration space is a two dimensional surface S. We also suppose that the particle feels the effect of an homogeneous magnetic field perpendicular to the surface S. In the first case S = R × SL1, the infinite cylinder of circumference L, corresponding to periodic boundary conditions, while in the second one S = R2. In both cases the particle feels the effect of an additional suitable potential. We are thus left with the study of two specific classes of Schrödinger operators. The operator of the first class generates the dynamics of the particle when it is submitted to an Anderson-type random potential, as well as to a non random potential confining the particle along the cylinder axis in an interval of length L. In this case we describe the spectrum and classify it by the quantum mechanical current carried by the corresponding eigenfunctions. We prove that there are spectral regions in which all the eigenvalues have an order one current with respect to L, and spectral regions where eigenvalues with order one current and eigenvalues with infinitesimal current with respect to L are intermixed. These results are relevant for the theory of the integer quantum Hall effect. The second Schrödinger operator class corresponds to the physical situation where the potential is the sum of a "local" potential and of a potential due to a weak constant electric field F. In this case we show that the resonant states, induced by the electric field, decay exponentially at a rate given by the imaginary part of the eigenvalues of some non self-adjoint operator. Moreover we prove an upper bound on this imaginary part that turns out to be of order exp(-1/F2) as F goes to zero. Therefore the lifetime of the resonant states is at least of order exp(-1/F2).

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