Study On Electric Potential And Charge Distribution Of The Systems With Conducting Sphere In An Applied Electric Field

The electrostatic induction will happen when a conducting sphere is placed in a homogeneous electric field.The electric field in any point can be taken as the sum of the homogeneous field and the field produced by an electric dipole moment in the center of the sphere.However,if the conducting sphere closes to one of the electrode,the induced charge on the sphere will affect the distribution of charge on the electrode.Thereof,the electric field distribution will change.For another case where two identical conducting spheres in an homogeneous electric field close to each other,the induced charge on the two spheres will affect both the charge distribution on the spheres and the electric field distribution in the space.At present,the methods to calculate and analyze these systems include approximation of dipole moment,finite element method,multi-pole moment model,and multiple image method.Any method has its advantage and disadvantage considering both calculation precision and computation rate.Multiple image method can ensure both high computation rate and calculation precision.It can also give an acceptable physical picture.In this work,based on the multiple image method,both the case including a plate electrode and a conducting sphere and the case including two identical conducting sphere in an applied homogeneous field are analyzed and discussed.There are many relevant works on the system with isolated conducting sphere,but there is little work to study the system with fixed electric potential.For the system with fixed potential,it is convenient to calculate by finite element method.However,the multiple image method attracts more and more attention because of its high calculation rate.The former research thought that the potential of the sphere only depends on the charge on the sphere.Actually,the potential of the sphere should depends on the homogeneous electric field,thedistance between the sphere and the electrode,and the potential of the electrode.In this work,the multiple image method is advanced to analyze both the case of one conducting sphere near an electrode and the case of two close conducting spheres with fixed potentials.Firstly,the image charge distribution is calculated.The electric field and potential distributions are calculated based on the image charge distribution.After that,the relation and corresponding formula between the potentials and the first order image charge are given out.Comparing the formula we got and that used in the previous work,it can be found that the value of the first order charge will affect the result,but the previous work neglected the influence to the first order charge by the potential of the electrode.Corresponding electric field and potential distribution must be calculated by the method proposed here considering potentials of both the electrode and the sphere.Result shows that the difference can not be neglected,especially when the sphere closes to the electrode.This work clarifies the key factors that determine the electric field and potential distribution of the system with conducting sphere in a homogeneous electric field.The relation between the first order image and the potential difference is given out.This work can extend the application of the multiple image method.