4 - Electrostatics

Summary

Introduction

Everyone has empirical knowledge of electrostatic and electromagnetic phenomena based on experiences such as the buildup of static charge on a comb or nature's grand displays of lightning and the auroras borealis and australis. Less obvious but no less familiar are the stabilizing effects of electrostatic forces in colloidal suspensions. Clay particles and silt carried in suspensions by rivers coagulate upon encountering the higher salt concentration of the sea to form huge deltas. Electrostatic stabilization is also responsible for the long shelf-life of certain latex paints. Needless to say, electrostatic forces play central roles in the behaviour of biological systems. Despite such diversity, electromagnetic and electrostatic phenomena can be understood in terms of the elegant theory embodied in Maxwell's equations. Here we take these equations as axioms and proceed deductively.

The presentation is organized as follows. First the equations governing quasi-static electric fields are set out. Starting with the balance laws and conditions prescribed at boundaries where electrical properties change abruptly, we are led to discuss dielectrics, polarization, free charge, and the electrical stress embodied in Maxwell's stress tensor. Then emphasis shifts to the electrical double layer and mathematical models describing its behavior. Here layers of charge are immobilized on a surface, while ions in the adjacent solution move freely under the influence of electrical forces and Brownian motion. After studying matters near a single surface, we turn our attention to the region between two surfaces and electrostatic forces between macroscopic particles in solutions containing dissolved ions.