Some Difficult Problems In The Electromagnetic Field

This paper has corrected and remedied the defect of some books and articles' theory of Electromagnetism by studying some difficult problems in the Electromagnetism as follows:1. The solution for the distribution of potential internal and external the dielectric ellipsoid has been obtained by means of ellipsoidal coordinates,and has obtainted the expression of the polarization field strength in the dielectric ellipsoid,calculated the included angle value of polarization vector and the external field vector,making programe to compute to get the relation shetch between the included angle value of polarization vector and the external field vector and we have discussed the result and hold that the direction of polarization field strength with that of the external field don't always strict antiparallel.2. The series solution of the eccentric spherical capacitor's capacitance has been obtained based on the bispherical coordinate system and strict derivetion,and through making programe to compute to get the numerical relation between the capacitance and the eccentrity,pionted out that the capacitance not let up but enlarged with the gain of eccentricity.3. The electrostatic problem of bispherical conductors is soluted strictly with bispherical coordinate system ,which remedies the defect of the image method that has no general formular of the result,proves the coherence of the image method and analytic method and demonstrates the calculating method of electrostatic energy between the electrostatic bispherical conductors.4. By using the numerical methods to study the magnetic field distribution and inductance out of the axis of a limited long spiral line tube,we have abtained the numerical solutionof them and also discussed it.perfect that of the insufficient of some general eleltromagnetic books and references .5. The electromagnetic scattering form the rough surface using the small slope approximation is investigated, this theory gives a systematic expansion of the scattering cross section that can be interpreted as series in generalized surface slope, the bistatic scattering cross sections for Gaussian conducting rough surface under the first, second and third-order small slope approximation are obtained. The results by the small slope approximation are also compared with that of the Kirchhoffapproximation with shadowing effect considered and the experimental data. It is found that the small slope approximation is more accurate for the whole incident angle and the numerical results also show good agreement with the experimental data for the large scattering angle.6.Based on the mathematical physics theory, this paper deals with the solution of equipotential surfaces of charged conductors of two parallel cylinders with eccentric axes or separated ones unitedly. By means of combination of conformal mapping, separation of variables,we have obtained the strict solution which can be expressed completely by elementary, functions and plotted the relative equipotential line maps; meanwhile, we have made the necessary discussion.