Introduction

The previous sub-topic of this unit, Electric Charges and Fields, described the electrostatic field in terms of a VECTOR quantity, the electric field intensity $\vec{E}$, whose magnitude and direction had to be tracked at every point in space. This sub-topic introduces a companion SCALAR description of the very same field, electric potential $V$, and shows that a great deal of electrostatics -- work done in moving a charge, the equilibrium configuration of charges, the behaviour of conductors and insulators, and the storage of electrical energy in a device -- becomes considerably easier to handle once it is expressed through this single scalar quantity rather than through the full vector field. Starting from the definition of potential and potential difference (Section 2.2), the chapter derives the exact relationship connecting $\vec{E}$ and $V$ (Section 2.3), works out the potential due to a point charge, a dipole, and an arbitrary system of point charges (Sections 2.4-2.6), and introduces equipotential surfaces as a geometric picture of the field (Section 2.7). It then turns to electrostatic potential energy, first for a simple system of two point charges and then for a dipole placed in an external field (Sections 2.8-2.9), before examining how conductors and insulators respond differently to an external field at the level of their free and bound charges (Sections 2.10-2.11). The second half of the chapter is built around the capacitor -- a device purpose-built to store charge and electrical energy -- covering its basic definition, the parallel plate capacitor with and without a dielectric medium, spherical capacitors, series and parallel combinations, the energy stored in a charged capacitor, and finally a brief, qualitative look at where capacitors show up in everyday devices (Sections 2.12-2.17).