A dielectric image method is proposed which uses the polarization charges around a point charge and at dielectric boundaries. The problem of a point charge and a dielectric plate in different dielectric media is solved. The method requires only fundamental algebra and integral calculus. The solution of this problem is compared with the solution by separation of variables.
Electrostatic problems having a simple dielectric boundary are solved using the concept of polarization charge. Using elementary mathematics, it is shown that the electrostatic field due to the total polarization charge distributed on a boundary surface between two homogeneous and isotropic dielectrics, is equivalent to that due to the lumped image charge used conventionally in teaching these problems. The demonstration of the equivalence of the surface polarization charge to the image charge will help students to understand the physical base of the image charge. Two problems are treated: a plane dielectric boundary, and a dielectric sphere immersed in a uniform field.
An expression for a magnetic field of a current ring is presented. The current distribution in the cross section of a thin current ring is expressed as a two-dimensional delta function and is substituted in Poisson's equation for vector potential. The expression, derived from the solution of the equation, is given in the form of an integral with respect to a parameter. The expression is applied to the problem of the magnetization current on the surface of an iron core and to the problem of the self-inductance of an aircore coil.
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