Near approach of two conducting spheres: Enhancement of external electric field

An external electric field applied to two uncharged conducting spheres in close approach is amplified (by charge separation on the spheres) in the region between the spheres. This enhancement increases without limit as the separation between the spheres decreases. We calculate the enhancement factor analytically, for spheres of radii a and b. A compact formula is given for the case where the separation s between the spheres is small compared to both a and b.     

Electrostatic interaction between two conducting spheres

In the paper we consider the problem of the electrostatic interaction between two charged conducting spheres with arbitrary electrical charges and radiuses. Using the image charges method we determine exact analytical formulas for the force F and for the potential energy W of the interaction between these two spheres as well as for the potential V of the electromagnetic field in an arbitrary point created by them. Our formulas lead to Coulomb’s law for point charges.We theoretically prove the experimentally shown fact that two spheres with the same type (positive or negative) of charges can also attract each other.     

On the polarization interaction between two closely spaced conducting spheres in a uniform electrostatic field

An electrostatic interaction between two separate, grounded, uncharged, perfectly conducting spheres of different radii in a uniform electrostatic field is investigated. It is shown that at a small center-to-center distance of the spheres, the force of the polarization interaction between the spheres depends appreciably more weakly on that distance in comparison to the force of the electrostatic interaction of two elementary dipoles as it should be in view of the interaction between two like polarization charges.     

On the force of electrostatic interaction between two conducting spheres

A compact solution is obtained to the problem on the force of interaction between two conducting spheres with preset charges on their surfaces in zero external field. The derivation is based on exact solution of the problem of the potential distribution in the bispherical coordinate system. The expression for the force was derived by differentiating the potential energy of interaction between the spheres with respect to the distance between their centers. It is shown using numerical calculations that with decreasing distance between the spheres, the ratio of their charges for which the forces of interaction between the charges are zero tends to the ratio of the charges of contacting spheres. It follows hence that for any ratio of charges of the same polarity, which differs from the ratio of charges of the contacting spheres, there always exists a small distance between the spheres, at which they attract each other.     

Two identical conducting spheres with same potential in a uniform electric field

Interaction, polarization, and charges or electric field distribution of conducting spheres in applied electric field are in many fields including electrorheological fluids, electrophoresis, and electrical engineering. A system with two equipotential conducting spheres in an applied uniform electric field is analyzed by image method. A new method is put forward to calculate the image charges distribution when using image method, which ensures the validity of image method to analyze equipotential cases. An apparatus is constructed to measure the force experimentally as well. Results show that the distribution of electric field and electric interaction are different with the case not equipotential.     

Polarizability of two conducting spheres

Exact series expressions are obtained for the longitudinal and transverse polarizabilities of a system of two conducting spheres, for arbitrary sphere radii and separation. In the important case of close approach, where the exact series converge slowly, approximate analytical expressions are obtained. These analytical expressions become more accurate as the distance between the spheres gets small compared to the sphere radii, and reduce to the known analytic values at sphere contact.     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

Numerical investigation of space charge electric field for a sheet electron beam between two conducting planes

Analytical and numerical study of the stability of sheet electron beam in periodically cusped magnetic field (PCM) is made. The beam has been considered as having diffused density profile. The conditions for beam focusing are discussed.     

Polarization of two close metal spheres in an external homogeneous electric field

The dipole moment of each of two uncharged conducting spheres with radius R in an external electric field was calculated. The distance between the centers of the spheres is 2l. It was shown that, if R/l≲0.8, the influence of higher multipole moments is negligible.     

Relation between contiguous Mie coefficients for perfectly conducting spheres

It is shown that when the size parameter x = ka in the scattering of electromagnetic waves by a perfectly conducting sphere is equal to an integer n, the Mie coefficients a_n and a_n−1 are equal. It is also shown that the other Mie coefficient b_n cannot be equal to b_n−1 for any finite x. The latter conclusion also holds in the case of scattering of a scalar particle by a hard sphere in quantum mechanics.     

On interaction of two closely spaced charged conducting spheres

Electrostatic interaction between two charged conducting spheres is analyzed in the case of a small spacing between them, when the polarization effects are significant. It is shown that short-range polarization forces result in the attraction of the like-charged spheres. At a sufficiently small spacing, this attraction replaces repulsive forces acting on like charges.     

Hydrodynamic interaction between two spheres

We evaluate the hydrodynamic interaction tensors for two spheres of unequal size and for general mixed slip-stick boundary conditions. A method of reflections leads to a series expansion for the diffusion tensors in powers of the inverse distance l^?1 between sphere centers and explicit results are derived through terms of order l^?7. It turns out that the series expansion for the diffusion tensors converges much more rapidly than that for the friction tensors.     

Imaging of conducting media by the electric field tomography method

The paper describes physical principles of electric field tomography that allows information on spatial distribution of conductivity and permittivity of an object to be obtained in a noncontact way using the quasi-static electric field. Specific features in implementation of the method are pointed out, and the results of imaging test objects are given.     

两个同心旋转球之间流动的谱方法

利用Stokes算子的特征函数作为基函数,用谱Galerkin方法对两个同心球之间的粘性不可压缩流动进行了研究,并作了数值模拟,并且利用谱方法得到了一个Lorenz型方程,分析了它的稳定性,证明了其吸引子的存在性。     

Relation between space-charge-limiting current and electric field enhancement factor at curved surface cathode

A two-dimensional solution of space-charge-limiting current for a high current vacuum diode with a spherical cathode is presented. The relation between space-charge-limiting current and electric field enhancement factor at the cathode surface for the diode with a curved surface cathode is also discussed. It is shown that compared with the current given by the conventional Child—Langmuir law, which describes the one-dimensional space-charege-limiting current, the two-dimensional space-charge-limiting current in such a diode is enhanced due to the electric-field enhancement along the cathode surface. Among practical parameter ranges, enhancement factor η_b approximately satisfies η_b ≈ Aβⁿ, where β is the electric field enhancement factor at the cathode surface, and n is a constant between 1 and 2, which is confirmed to be universal for the diodes with curved surface cathodes.     

Electric field enhancement between two parallel cylinders due to plasmonic resonance

We theoretically examine the electric field enhancement in the narrow gap between two parallel cylinders due to the plasmonic resonance. The resonance condition and the field enhancement factor are found explicitly. It is shown that the resonance occurs at frequencies lower than the plasma frequency. This effect results from the special geometry: the gap width between parallel cylinders is much smaller than their radii. It is also shown that the enhancement coefficient is much larger than the one for a single cylinder and is determined together with the resonance frequency by the system geometry.     

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.     

Nonuniform quasistatic electric field in a weakly conducting anisotropic medium

The intensity distribution of a nonuniform electric field in a quadrupole electrooptic deflector, the properties of the medium in which are described simultaneously by permittivity and conductivity tensors which are not proportional to each other, is calculated as a function of the phase of the ac control voltage. It is shown that the space charge arising in this case is phase-shifted relative to the control voltage. The computational results are compared with experimental data. Zh. Tekh. Fiz. 67, 51–54 (October 1997)     

Cascaded plasmonic nanorod antenna for large broadband local electric field enhancement

We propose a cascaded plasmonic nanorod antenna for large broadband electric near-field enhancement. The structure has one big gold nanorod on each side of a small two-wire antenna which consists of two small gold nanorods. For each small nanorod, the enhanced and broadened optical response can be obtained due to the efficient energy transfer from its adjacent big nanorod through strong plasmonic near-field coupling. Thus, the electric field intensity of the cascaded antenna is significantly larger and broader than that of the individual small two-wire antenna. The resonant position, field intensity enhancement, and spectral width of the cascaded antenna are highly tunable by varying the geometry of the system. The quantum efficiency of the cascaded antenna is also greatly enhanced compared with that of the small antenna. Our results are important for the applications in field-enhanced spectroscopy.     

共焦椭圆导体简间的电场与电容

根据共焦椭圆函数,将拉普拉斯方程的求解变为积分运算,进而导出了共焦椭圆筒间的电容与电场分布.