Chapter 4 - Gauss's Law: Flux and Charge Are Related

Abstract

Electricity is difficult to comprehend in part because we cannot actually see the electric charge that produces specific electrical effects. However, by tracing the path of the field lines due to a set of electric charges, one could locate the charges, and even determine their magnitudes. This is the basis of field-line drawing rule. For more precision, field lines can be replaced by electric flux. A consequence of the Gauss's law is that if the electric flux leaving the surface of an object is known, either by calculation or by measurement, one can determine the electric charge within that object. The Gauss's law allows the determination of the total or net electric charge inside the potato-shaped Gaussian surface, without actually measuring that charge. Charge distributions of three types produce a flux that is uniform or zero for all parts of an appropriately chosen Gaussian surface: centro-symmetric charge distributions with spherical, cylindrical, and planar symmetry. The Gauss's law and the knowledge of the charge enable the deduction of the magnitude of the electric field for these surfaces. The chapter proves Gauss's law by using the concept of solid angle.