Distribution of electric field in the round hole of plane capacitor

A planar capacitor with a round hole, filled by electrorheological fluid, can be used to design valves controlled by an electric field. To design valves effectively, the distribution of the electric field within the hole must be known. When the distribution along the axis of the hole is known, the electric field can be calculated at any point inside the hole. Relative coordinates, such as the ratio of values of real coordinates to the half height of the capacitor, and relative parameters, such as the ratio of the values of the outside electric field to the field inside the capacitor, are utilized in this study. The electric field on the axis of the hole is found in two steps. First, the electric field along the axis of symmetry between two plane capacitors is calculated by finding the field distribution near the edge of the detached plane of a two-plane capacitor, then the redistribution of the charges on the plate of the capacitor, due to influence of the neighbouring capacitor plate is evaluated. Second, the electric field along the axis of the round hole is calculated, thus allowing us to evaluate an alternative mechanism for charge redistribution from the plane parallel case to the case of a field with axial symmetry. Results show that the field in the hole becomes weaker when the hole is filled with a liquid of relative permittivity higher than unity. Diminution of the field can be avoided by filling the area on the capacitor with the medium of the same or greater permittivity.