Surface Forces Induced by Point Charge in a Multilayered Dielectric System

• Author / Creator

  Rahman, Hasib I

• Local surface force density and total surface force induced by a single point charge embedded in a three-layered homogeneous dielectric system with infinite planar interfaces are calculated using the Maxwell Stress Tensor formulation. The tensor is expressed in terms of the electric field which is first derived from solving the electric potential in all domains. The electric potentials are obtained in closed form using the Hankel transformation. Nondimensionalization of the solutions for electric potential, local surface force density and total surface force reduces the governing parameters into three scalars: a normalized charge location and two dielectric constant ratios. These dimensionless parameters are varied to analyze their influences. The numerical parametric study reveals interesting, coupled influences of theses parameters on the distribution of electric potential. It was also found that the two ratios between the dielectric constants of the three layers play a primary role in the forces: they determine the direction of the surface force density and total surface force, as well as the distribution of the surface force density, which can vary monotonically or non-monotonically with the radial position. The position of the point charge, on the other hand, only affects the magnitude of the surface forces. Due to the linear nature of the electrostatic problem, the formulations presented here can be extended to establish a theoretical framework for modeling contact adhesion, where interfacial adhesive forces arise from a distribution of charges. An example to solve this type of problem is presented where a pair of equal and opposite charges are considered in the same model. Comparison between these two systems show that the addition of an extra charge introduces significant changes in the magnitude of surface force density while their directions are found the same in both systems. The results also reveal that the total surface force can be altered both qualitatively and quantitatively by the extra charge. This additional charge can increase or decrease the net surface forces depending on the charge location and the dielectric constant ratios of the three layers.

• Subjects / Keywords

  • Maxwell Stress Tensor
  • Surface Force
  • Hankel transform
  • Multilayered Dielectric

• Graduation date

  Fall 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R37D2QC7X

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.