Research On Interaction Forces And Local Field Of Two Equal Size Conducting Spheres In The Electric Field

In practice, it is importance of research on the interaction forces between spheres exposed to electric field, such as electrostatic separation, electrorheological fluids, microand nano- electromechanical systems, etc. Determination of the interaction forces and local field between two conducting spheres subjected to an uniform electric field is one of the old and classic boundary value problems in physics. The difficulty of the problem comes from the mathematical treatment of the mutual electric induction between the biospheres, which becomes quite strong when the spheres are close to touching, and makes the interaction forces dependent, in a complicated way, on the separations of the spheres. Rigorous solutions for the problem can be achieved by solving Laplace’s equation in biospherical coordinates. However, the results are often expressed in infinite integrals or special functions, being inconvenient for practical use. Numerical calculations can also be performed by employing multipolar expansions or the image charge method, but divergence difficulty is encountered as the spheres approaching very close. Here analyses for the problem are made by using the image dipole method. Contributions from the mutual electric induction of the spheres are involved in the imaging process for dipoles and charges. Summing up the forces and electric field caused by all image charges and image dipoles respectively, the interaction forces and local field between two conducting spheres are obtained in simple functions including series of hyperbolic functions first. Then the relationship of the interaction forces and local field strength with the separation are analyzed and, furtherly, asymptotic behaviors of the interaction forces are discussed by using Abel-Plana formula at small and large separations. Good agreement obtained with the results both of experiment and multipolar expansions, which proves the effectiveness of the method proposed here.For the polarization of two conducting spheres applied by external electric field, serval methods commonly used to solve the problem are analyzed and compared firstly. And then the polarization process is explored by employing of image dipole method, and respectively, the dipole moment of each sphere exposed in both uniform and point dipole electric field are obtained finally.The interaction forces between two spheres applied by an uniform electric field, taking the longitudinal case with spheres grounded as exemplification, are calculated by image dipole method. Furtherly, the relationship of forces and separation gap of spheres are discussed and so as to the impact of whether grounded. Asymptotic behaviors is accessed by using of Abel-Plana formula and the conclusions are extended to other cases. And the local field strength variation laws is obtained by the illustration at vertical apex of spheres. And the results shows that all of the direction of external field, whether spheres grounded and the separation gap have notable impact of both interaction forces and local field.Image dipole method is employed to analyze the interaction forces of two identical spheres in point dipole electric field, which indicates that the interaction forces of two spheres appears as repelling force and dominated by the effect of point dipole. In the end, the local field in the middle area of two spheres is analyzed and the change rele is obtained.