The Electric Field in the Round Hole of the Air Plane Capacitor

Abstract

The round hole in the plain capacitor can be applied for construction of the valves controlling by electric field. It is important to know distribution of electric field in the hole. The electric field in the round hole can be investigated using known distribution of field near the edge of plain capacitor. The investigation is performed using the relative coordinates as relations of values of real coordinates to the half thickness of capacitor and the relative parameters as relations the values of field to the value of field inside of the capacitor. The field in any point of hole can be calculated when the distribution on the axis of the hole is known. The field on the axis of hole can be calculated using the distribution on the axis of symmetry between two plain capacitors. This field is the superposition of the fields near the both capacitors, which must be multiplied by two coefficients: the coefficient which evaluates the change of distribution of the charges on the plates of capacitor and the coefficient which evaluates different mechanism of formation of total field in the plane parallel field and in the field with axial symmetry. The expressions of both factors are obtained. The expressions of total field and it components are obtained for the important in the practice case when the thickness of capacitor is equal to diameter of hole. The radial component is approximate by linear law and the vertical component – by parabolic law. Ill. 3, bibl. 2 (in English; summaries in Lithuanian, English and Russian).