Gauss’s Law: Charges and Electric Fields

Abstract

This chapter discusses electrostatics and Gauss’ law. The electric charge, Q, is an essential concept in electrostatics. There are two types of charge, positive and negative. Like charges repel and opposite charges attract. Importantly, charge is conserved: starting from zero charge, if you isolate a charge Q somewhere, there has to be an equal and opposite charge − Q somewhere else. Charge is also quantized in integer multiples of the electronic charge. Electric charges create electric fields, E, which constitute another essential concept in electrostatics. The electric field, E, is a “vector field”. That is, E is a vector that exists at every point in space. Positive charge can be conceived to be the source of electric field, and negative charge the sink. To understand how electric charges create electric fields, this chapter will focus on understanding and applying Gauss’s law to find the electric field for different charge configurations in situations with high symmetry (e.g. spheres, cylinders, planes of charges). Because Gauss’ law is a linear equation, electric fields obey the principle of superposition, implying that the electric field of a collection of charges is equal to the sum of the electric fields of each charge in the collection.