GAUSS LAW AND ITS APPLICATIONS

This section builds, in stages, one of the most powerful tools in electrostatics. It starts from the simple geometric idea of electric flux -- essentially a count of how many field lines pass through a given surface -- extends that idea to flux through closed surfaces of arbitrary shape, and arrives at Gauss's law, a general and exact relation between the total flux through any closed surface and the net electric charge enclosed within it. Although Gauss's law can be derived directly from Coulomb's law and is therefore not new physics, it becomes an extremely efficient computational shortcut whenever a charge distribution possesses a high degree of symmetry (spherical, cylindrical, or planar), letting the electric field be found in a few lines of algebra for c …