Modeling analysis of the electrostatic interaction between a nth-order electric multipole moment and dielectric layers utilizing the image multipole method

Accurate determination of the electrostatic force exerted on multipole moments is essential in comprehending the interaction between charged bodies and dielectric layers. A comprehensive solution is presented in this study for the calculation of the electric potential, field, and force generated by nth-order electric multipole above a semi-infinite dielectric body covered by a dielectric layer using the image multipole method. The present study investigates the impact of dielectric thickness, permittivity, and separation distance on the electrostatic interaction between an electric multipole moment and a semi-infinite dielectric body. The calculation results indicate that as the thickness of the dielectric layer increases and the dielectric constant of the surrounding medium surpasses that of the dielectric layer, the electrostatic attractive force undergoes a transition to a repulsive force. The magnitude of the electrostatic force acting on a nth-order electric multipole moment is directly proportional to the square of the value of the electric multipole moment and inversely proportional to the 2 (n+1) power of the distance.