Electric Field for a Zero Contact Angle (Smooth Contact)

Abstract

In the case of smooth contact with a zero contact angle between a solid dielectric and a surface, the field at the point of contact exhibits neither a singularity (an infinitely high value) nor a zero value, but it can be significantly high. For the simple case of a spherical or cylindrical conductor resting on an infinitely thick solid dielectric, the field strength at the contact point is expressed by a quadratic function of ε _s on the gas side and by a linear function of ε _s on the solid side. The ratio ε _s is equal to ε _B /ε _A , where ε _B and ε _A are, respectively, the dielectric constant, or relative permittivity, of a solid and a surrounding medium. This field behavior was derived analytically by the classical image method by T. Takuma and T. Kawamoto [1, 2]. However, there had been several papers dealing with the field behavior for a zero contact angle published earlier, and these are briefly mentioned here. Further details are provided by T. Takuma and T. Kawamoto [1].