Field enhancement by bubbles in dielectrics Package Electrostatics Toolkit Input files Bubbles.MIN, Bubbles.EIN, Bubbles.BAT, Bubbles.SCR Download Bubbles.zip Description Calculation of the field enhancement caused by a dielectric sphere in a dielectric medium with a uniform applied electric field. The example illustrates two techniques: Using scaling laws to derive general results from specific numerical calculations. Setting up controls for automatic calculations to perform a complete study in a background run. Results The top figure shows equipotential lines and a detail of the distribution of |E| for a sphere with high dielectric constant in a medium with moderate dielectric constant (e.g., water droplet in transformer oil). Electric field enhancement at the poles of the sphere (relative to the electric field vector) may approach a factor of 3. The lower figure is a generalized graph of enhancement as a function of the ratio of the dielectric constant in the bubble to that of the medium. The graph holds for spheres of any radius. The solid line for enhancement inside the bubble is a theoretical prediction. Comments In the radial coordinates, the half circle in the upper figure represents a sphere. This tutorial describes the calculations in detail: How not to do a finite-element calculation.