Electrostatic potential in cylindrical dielectric media using the image charge method

We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.     

点电荷与介质球系统电势的计算和讨论

计算了点电荷与介质球系统的电势．指出点电荷与导体球、点电荷与无限大导体平面或介质分界平面均匀外电场中有导体球或介质球系统的电势都可由点电荷与介质球系统的电势给出。     

Multiple Image Method for the Two Conductor Spheres in a Uniform Electrostatic Field

A method using multiple mirror images of point charges is put forward to analyze the polarization of two identical conductor spheres in a uniform electrostatic field. By use of the method, the electric field distribution and the interaction force between two spheres can be calculated accurately even for very small gap between two spheres. Our results show that the magnitude of the product of the gap between two spheres and the local electric field in the center of the gap is approximately in the same order and the interaction between two spheres increases very fast as the two spheres are close to each other. We also show that the interaction force between two conductor spheres is almost same with that between two dielectric spheres with high permittivity.     

Capacitance of an elliptical disk on a semi-infinite dielectric material

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.     

Microscopic theory of a transition layer on the ideal surface of semiinfinite dielectric media and the near-field effect

The microscopic theory of a transitional layer on the ideal surface of a semi-infinite absorbing or nonabsorbing isotropic dielectric is developed within the framework of classical optics when the polarization vector of the medium is a linear function of the electric field strength inside the medium. The concentration of atoms (molecules) of the medium and their polarizability are independent of coordinates and are constant inside the medium and close to its surface. The consideration is carried out within the framework of the concept of a discrete-continuous dielectric, in which the fields of dipoles of discretely distributed atoms (molecules) inside the Lorentz sphere surrounding the observation point are taken into account. The near-field effect is shown to result in a nonexponential behavior of the field nearby the surface. The thickness of the transitional layer can be found from experimental values of the reflected wave amplitude.     

Modelling of isotropic double negative media for microwave applications

A composite medium consisting of two sublattices of dielectric spherical particles of high permittivity and different radii embedded in a dielectric matrix of smaller permittivity are considered. It has been shown that such a composite medium reveals properties of an isotropic double negative media (DNG) in a limited frequency range, when resonance oscillations of H_III mode in one kind of particles and E_III mode in another kind of particles are excited simultaneously. The E_III resonance and the H_III resonance give rise to the magnetic dipole momentum and the electric dipole momentum correspondingly. Averaging the magnetic momentum and the electric momentum over the cells belonging to the appropriate spherical particles gives the negative permittivity and permeability. The model of diffraction of a plane electromagnetic wave on a dielectric sphere is presented and compared with the mixing rule based consideration. The results obtained are rather close. Distribution of the electromagnetic wave outside the sphere is calculated. Influence of the dispersion of the sphere size and the dielectric permittivity on the effective parameters of the DNG material is estimated.     

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach

A numerical methodology to simulate two-phase electrohydrodynamic flows under the volume-of-fluid paradigm is proposed. The electric force in such systems acts only at the interface and is zero elsewhere in the two fluids. Continuum surface force representations are derived for the electric field force in a system of dielectric–dielectric and conducting–conducting fluids. On the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region (interface). It is shown that a wrong choice of interpolation scheme (weighted arithmetic mean) may lead to a transition region thickness dependent electric field in the bulk. We simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed. A coupled level set and volume-of-fluid (CLSVOF) algorithm has been used for simulations presented here.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

Force and torque on a sphere with electric dipole moment moving in a dielectric fluid in the presence of a uniform magnetic field

The torque exerted by a magnetic field on a sphere with permanent electric dipole moment moving steadily in a dielectric fluid is calculated to lowest order in the dipole moment. Hence the force exerted on a steadily rotating sphere with electric dipole moment is found by Onsager symmetry. The modification from the vacuum values of torque and force depends only on the slip parameter and the static dielectric constant of the fluid. It is suggested that for a macroscopic ferro electric sphere the calculated effects could be measured experimentally without great difficulty.     

Dielectric relaxation in deuterated triglycine sulfate crystals

A study has been made of the slow relaxation of the dielectric permittivity of deuterated triglycine sulfate (DTGS) initiated by application of a dc electric field. The field and temperature dependences of the relaxation time associated with domain-wall motion were obtained. The effect of the internal electric field on relaxation processes is seen in different behavior of the field and temperature dependences under different orientations of the external field. The existence in DTGS crystals of two temperature regions of domain-structure rearrangement lying 7–8 and 15–18 °C below the Curie point has been established. Fiz. Tverd. Tela (St. Petersburg) 40, 1542–1545 (August 1998)     

电场作用下离散相行为研究

为明晰电场对两相系统中离散相的作用,本文针对均匀电场作用下两相系统中的单个离散相的行为进行了可视化试验研究及数值模拟。通过建立电场数学模型。得到了均匀电场作用下两相系统的电场分布;运用电应力表面积分的方法求得了离散相所受的电场力。并于试验中观察了不同粒径的离散相在电场作用下的运动情况,其试验结果与数值计算结果基本吻合。     

Non-inertial electromagnetic effects in matter. Gyromagnetic effect

Non-inertial electromagnetic effects in matter, i.e. electromagnetic fields created by a non-inertial motion of material bodies, are discussed within the Drude–Lorentz (plasma) model of matter polarization. It is shown that an oscillatory motion of a point-like body, or wavelike motion in an extended body gives rise to electromagnetic fields with the same frequency as the frequency of the original motion, while shock-like movements of a point-like body generate electromagnetic fields with the characteristic (atomic scale) frequency of the bodies. The polarization of a rigid body induced by rotations is discussed in various circumstances. A uniform rotation produces a static electric field in a dielectric and a stationary current (and a static magnetic field) in a conductor. The latter corresponds to the gyromagnetic effect (while the former may be called the gyroelectric effect). Both fields are computed for a sphere and the gyromagnetic coefficient is derived. A non-uniform rotation induces emission of electromagnetic fields. The equations of motion for the polarization are linearized for slight non-uniformities of the angular velocity and solved both for a dielectric and a conducting sphere. The electromagnetic field emitted by a dielectric spherically shaped body in (a slightly) non-uniform rotation has the characteristic (atomic scale) frequency of the body (slightly shifted by the uniform part of the angular frequency). In the same conditions, a conducting sphere emits an electromagnetic field whose frequency is double the uniform part of the angular frequency.     

Local fields in a soft matter bubble

The electric field created by a point dipole located in a dielectric void (“bubble”) is calculated. We consider a continuous profile of the medium permittivity and find that, at large distances, the effective dipole field depends on the model chosen for the bubble walls, in particular their thickness. A boundary layer model is analyzed that gives good agreement with numerical calculations. Our results shed light on the local field correction that has attracted lot of interest lately.     

Effect of external electric field on crystalline structure and dielectric properties of Bi_(1.5)MgNb_(1.5)O_7 thin films

Bismuth-based cubic pyrochlore materials have attractive dielectric properties, especially dielectric tunability. The Bi_(1.5)MgNb_(1.5)O_7 ceramic samples were prepared by solid state reaction. The XRD results and SEM pictures prove the raw material are well mixed and co-fired and the BMN cubic pyrochlore is well crystallized, no second phase was found in the result. BMN thin film were fabricated by depositing BMN ceramic nanoparticles on the sapphire. The BMN thin film has a high dielectric tunability of 43% at a bias voltage of 1.5 MV/cm, with loss tangent lower than 0.009. A Raman study of BMN cubic pyrochlore reveals O′–A–O′and O–A–O bending modes contribute to 80% of dielectric permittivity,obstructing these modes such as applying external electric field can have apparent influence on dielectric constant. Berry Phase calculation results shows that A_2 O′tetrahedrons are more easy to distort under an external field. The A-site Mg have the highest displacement(0.765028 ?), followed by A-site Bi cations(0.346317 ?). Compared to zero-bias thin film,the biased one with A–O and A–O′bonds being stretched and external coulomb force applied on cations and anions, the dielectric constant under bias field dramatically decreased.     

The Casimir effect in a solid ball when εμ = 1

The Casimir surface force density on a solid ball is calculated assuming that the medium satisfies the relationship εμ = 1, ε being the permittivity and μ the permeability. Remarkably enough, the cutoff problems which otherwise plague calculations of the Casimir stress on dielectric nonmagnetic balls disappear, and one arrives at a cutoff independent, finite, and repulsive result for the force. When μ → 0 or μ → ∞ one finds exactly the same result as in the case of a perfectly conducting shell. Another virtue of the theory is that one may avoid the subtraction of contact terms, as the contact terms are simply vanishing. Finally, the theory is immediately applicable to a gluonic (nonquark) bag in QCD, assuming no gluonic interaction. The surface force in QCD becomes repulsive, just as in QED.     

Long-range surface plasmon polariton modes with a large field localized in a nanoscale gap

A planar five-layer waveguide with a metal-insulator (with the low permittivity)-metal structure embedded in a high-permittivity dielectric is theoretically studied. A long-range surface mode draws special attention because of its superior properties of low attenuation and a large field localized inside the nanoscale middle gap provided with permittivity-contrast. Effects of the surrounding permittivity and the metal film thickness are investigated, and the electric field amplitude in the gap can be dozens of times higher than that at the outer interfaces. This plasmonic structure may have potential applications in integrated photonic devices.     

Properties of the 3D photonic nanojet based on the refractive index of surroundings

We exhibit a three-dimensional （3D） photonic nanojet based on a dielectric microsphere irradiated by a plane wave with the finite-difference time-domain （FDTD） method. We investigate the influence of the refractive index of the surrounding on the properties of the nanojet by simulating the electric field distributions in it. The simulation results show that, by optimally choosing the size of the sphere and the ratio of the refractive indices of the sphere and the surrounding, the focus point can occur just on the surface of the sphere even if the refractive index of the surrounding is changed. Additionally, the peak amplitude of the nanojet increases with increasing the refractive index of the surrounding. However, the decay length and the jet width of the nanojet decrease simultaneously. These effects may have potential applications in observation or manipulation of nano-objects such as antibodies in biology. In nanojet-enabled optical data storage, the photonic nanojet may be also helpful for improving data-storage capacities and retrieval speed by controlling the field amplitude, the decay length, and jet width of the nanojet.     

Scattering from a coated nihility circular cylinder placed in chiral metamaterial

The scattering of electromagnetic plane wave from a coated nihility circular cylinder placed in chiral metamaterial is investigated. The nihility cylinder is coated with chiral or chiral-nihility metamaterial and the medium hosting the coated cylinder is also considered as chiral or chiral-nihility metamaterial. The vector wave equation is used to find out the solution for the fields scattered from the concentric chiral ciruclar cylinders immersed in chiral metamaterial. Inner chiral cylinder is reduced to nihility cylinder taking permittivity and permeability approaching to zero with chirality parameter equal to zero. Coated perfect electric conductor (PEC)/perfect magnetic conductor (PMC) are obtained by taking very large value of permittivity/permeability of the inner cylinder. Numerical results for fields reflected from coated nihility cylinder are compared with those obtained for coated PEC/PMC cylinder. Our results for the special case of dielectric coated nihility/PEC cylinders in free space are shown to be in agreement with already published results thus validating the scheme of analysis.     

The TEM101 mode laser beam—A powerful tool for optical levitation of various types of spheres

We point out in this paper that a TEM¹₀₁ mode laser beam is convenient to stably levitate either solid or hollow dielectric spheres or metallic ones. Except a sufficient incident flux, there is no stability condition required to levitate solid transparent spheres having a refractive index larger than the one of the surrounding medium. According to the beam and sphere diameters, the equilibrium position will be centered on the beam axis or off-axis. In the case of hollow dielectric or metallic spheres, the lateral stability requires specific conditions on sphere and beam diameters. These conditions are discussed and then experimentally shown by performing optical levitation of these various kinds of spheres either in vertical or in horizontal beams.     

Retarded Van der Waals potential between a conducting plane and a polarizable particle

The method of zero point energy is used to obtain the retarded Van der Waals potential between a perfectly conducting plane and a particle possessing both electric and magnetic polarizability. As a special case, the force between a conducting plane and a conducting sphere is obtained.