Calculation of the eddy current in a small conducting spherical particle

The eddy current in a small conducting spherical particle located in the field of a plane electromagnetic wave is calculated. The frequencies under study are bounded above by frequencies of the near IR region. The calculation is performed within the kinetic approach for a comparatively small particle (～10 nm) in which the skin effect can be neglected; the ratio of the particle size to the electron mean free path is assumed to be arbitrary. The reflection of the charge carriers from the sample boundary is assumed to be purely diffuse. The effect of temperature on the current density in the particle is studied.     

Scattering of a plane inhomogeneous electromagnetic wave by a spherical particle

We extend an analytical solution for the problem of diffraction of a plane wave by a spherical particle to the case of an inhomogeneous wave. Numerical examples showing a significant change in the scattered-wave structure compared with the case of diffraction of a homogeneous wave are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 72–81, January 2006.     

Force between the plates of a plane capacitor in a fluid: a rigorous thermodynamic analysis

Summary A critical analysis of the literature on the deduction of the well-known expression of the attractive force between the plates of a plane-parallel capacitor completely immersed in a linear dielectric fluid is presented. Then, rigorous deductions of this force are proposed. It is shown that, contrary to the statement reported in most references, no pressure difference exists between the fluid within the plates and the external fluid.     

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.     

Charge and force acting on a spherical body near a planar electrode in a polarizable conducting medium

A method for calculating electric fields in conducting polarizable media with interface is suggested. An integral equation for the density of surface charge induced at the interface is derived. The value of this density is used to find the field in the volume. The total charge induced at the interface and the force acting on a spherical body touching a planar electrode are calculated. It is found that the total charge and the force are alternating functions of the relative conductivity of the media; that is, both repulsion from and attraction to the electrode are possible depending on the conductivity. The near-electrode force acting on solid particles, bubbles, and drops in an immiscible liquid is studied experimentally.     

Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R_G and bond length a , and an impenetrable spherical colloid particle of radius R . Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R _G and R/a . The correction vanishes for the continuous chain model (i.e. in the limit R/R _G → 0 and R/a → ∞ but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).     

Casimir self-stress on a perfectly conducting spherical shell

The Casimir stress on a perfectly conducting uncharged sphere, due to occurrence of fluctuations in the electromagnetic field, is calculated using a source theory formulation. Two independent methods are employed: we compute (1) the total Casimir energy inside and outside the sphere, and (2) the radial component of the stress tensor on the surface. It is necessary to exercise care in allowing the field points to overlap; a correct limiting procedure supplies a “cutoff” in the frequency integration. In spite of numerous technical improvements, the result of Boyer, that the self-stress is repulsive (and not attractive as Casimir hoped), is confirmed unambiguously. The magnitude of the Casimir energy of a sphere of radius a is found, by numerical and analytic techniques, to be $\text{E = (}\text{h}\text{?}\text{c}\text{2a}\text{)(0.09235)}$, also in agreement with the very recent result of Balian and Duplantier.     

Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam

We present the analyses of radiation force and torque on a spherical particle illuminated by Laguerre-Gaussian beam. Since Laguerre-Gaussian beam has angular momentum, the particle can be rotated by illumination of Laguerre-Gaussian beam. Radiation forces and torques for a silver sphere and a silicon sphere near the silver substrate are analyzed. We found that the maximum torque on silicon sphere is about five times higher than the maximum torque on silver sphere and fine control of the focused spot is required to push the particle to the substrate.     

Adsorption of a polyampholyte on a charged spherical particle

We develop a scaling theory for a single polyampholyte chain adsorbed on a charged spherical particle in a theta-solvent. Adsorption of a polyampholyte molecule is due to its polarization in the electrostatic field of the particle. For large particles with sizes exceeding the thickness of the adsorbed layer, the conformations of the chain are similar to the one found for polyampholyte adsorption on charged planar surface. However, an adsorbed polyampholyte chain forms a self-similar flower-like structure near the particles with sizes smaller than its Gaussian size. These self-similar structures result from the balance of the polarization energy of loops and the excluded volume interactions between monomers. The structure of an adsorbed polyampholyte in the flower-like conformation is similar to that of a neutral star polymer. Received 3 March 2000 and Received in final form 5 July 2000     

对偏心球形电容器电容的严格计算

在双球坐标系下采用分离变量的方法严格求解了偏心球形电容器的电容,得到了它的级数解,并通过编制程序计算获得了偏心球形电容器的电容大小与偏心率之间的数值关系,指出了某些文献中的不当之处．     

Thermodynamic energy exchange in a moving plate capacitor

In this paper we describe an apparent paradox concerning a moving plate capacitor driven by thermal noise from a resistor. The plates are attracted together, but a demon restores the plates of the capacitor to their original position when the voltage across the capacitor is small-hence only small forces are present for the demon to work against. The demon has to work harder than this to avoid the situation of perpetual motion, but the open question is how? This is unsolved, however we explore the concept of a moving plate capacitor by examining the case where it is still excited by thermal noise, but where the restoring force on the capacitor plates is provided by a simple spring rather than some unknown demon. We display simulation results with interesting behavior, particularly where the capacitor plates collide with each other. (c) 2001 American Institute of Physics.     

Variational estimates in electrostatics. Capacitance of a plane capacitor

Simple variational inequalities for the capacitance of a plane capacitor, which demonstrate the effectiveness of the variational approach to problems of electrostatics which are usually explained only quantitatively, can be proven completely rigorously and simply with the variational inequalities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 96–99, August, 1984.     

Electrically induced flows in the vicinity of a dielectric stripe on a conducting plane

We report a theoretical and experimental study of the hydrodynamic flow induced by an a.c. electric field in the vicinity of a dielectric stripe deposited on a conducting plate. In the theoretical part, we model the stripe as a small change of the surface capacitance of the plate, and a perturbative approach is used to perform the calculations. This approach predicts an outwards rectified electro-osmotic slip along the surface that generates two steady counter-rotating rolls, the size of which decreases with the frequency. In the experimental section, we use tracers to determine the structure of the flow and investigate its dependence on the frequency and the amplitude of the applied voltage. The structure and amplitude of the observed flow compares satisfactorily with the theoretical analysis. This could guide the design of surface-controlled flows and help to understand the collective behavior of colloids near electrodes. Received 20 June 2002 RID="a" ID="a"e-mail: nadal@crpp.u-bordeaux.fr     

Reflection of a spherical wave from a plane surface

A simple approach to the reflection of a spherical sound wave from a locally reacting plane surface is developed. The theory is based on a generalization of the method of images, and expresses the reflected wave as a series in terms of the reciprocal of distance from the image source. Although no general proof that this form for the reflected wave satisfies the surface boundary condition to all orders is available, it has been shown that the first five terms of this solution does satisfy the boundary condition, and agrees with the existing exact solutions for this type of reflection.     

Analysis of radiation pressure exerted on a metallic particle within an evanescent field

Radiation pressure induced by an evanescent field was experimentally analyzed for a single submicrometer-sized gold particle. The force measurement was based on a thermodynamic analysis of Brownian motion by use of a three-dimensional position-sensing technique. The lateral radiation pressure could be ascribed to a scattering force, which was oriented in the same direction as the propagation vector of the incident laser beam. The potential profile in the longitudinal direction indicated that the gold particle was attracted to the high-intensity region of the evanescent field by a gradient force.     

Multipole polarizability of a graded spherical particle

We have studied the multipole polarizability of a graded spherical particle in a nonuniform electric field, in which the conductivity can vary radially inside the particle. The main objective of this work is to access the effects of multipole interactions at small interparticle separations, which can be important in non-dilute suspensions of functionally graded materials. The nonuniform electric field arises either from that applied on the particle or from the local field of all other particles. We developed a differential effective multipole moment approximation (DEMMA) to compute the multipole moment of a graded spherical particle in a nonuniform external field. Moreover, we compare the DEMMA results with the exact results of the power-law graded profile and the agreement is excellent. The extension to anisotropic DEMMA will be studied in an Appendix.