Introduction

In Class XI you studied Gauss' law, which relates the electric flux through any closed surface to the total electric charge it encloses:

where $\phi$ is the total electric flux coming out of a closed (Gaussian) surface and $q$ is the total charge enclosed within it.

Gauss' law is completely general — it holds for a Gaussian surface of ANY shape, enclosing ANY charge distribution — but it only becomes a genuinely PRACTICAL tool for actually computing the electric field $\vec{E}$ when the charge distribution has enough symmetry that a convenient Gaussian surface can be chosen to make the flux integral on the left simple to evaluate directly, rather than having to add up Coulomb's-law contributions from every bit of charge. This chapter puts that idea to work: it uses Gauss' law, together with a systematic procedure for choosing and exploiting the right Gaussian surface, to find the electric field of several symmetric charge distributions, and then builds on the field concept to develop electric potential and potential energy in the sections that follow.