Abstract: The total charges of conductors are usually given in the second and third boundary value problems of the electrostatic field, but the electric field cannot be directly solved due to the unknown charge density distribution on the conductor surface. Therefore, according to the linear relationship between the conductor charge and the electric potential in the electrostatic field, the second and third boundary value problems are transformed into the first boundary value problem, so as to realize the calculation of the above problems. On this basis, the finite element analyses of the electrostatic field are carried out to verify the effectiveness of the proposed method by taking the parallel two-wire system as the research object.

Key words: electrostatic fields, boundary value problems, finite element method, linear systems