Chapter 4: Electrostatics – Coulomb’s Law & Electric Fields

Building upon this, the chapter defines the electric field (E) as the vector force experienced per unit test charge at any given point. A shift from forces to energy is made through the introduction of electric potential (phi), a scalar field defined such that the work required to move a charge between two points is independent of the path taken, confirming that the electrostatic field is conservative. The electric field is shown to be mathematically related to the potential via the negative gradient of the potential. The concept of electric flux is then introduced as a measure of the outward "flow" of the electric field through a surface. This leads to a rigorous derivation of Gauss’ law, a cornerstone of electrostatics, which states that the total electric flux passing through any closed surface is directly proportional to the total electric charge contained within that volume, divided by the permittivity of free space. Gauss' law is also presented in its differential form, detailing the divergence of the electric field. This powerful tool is demonstrated by solving for the electric field of a uniformly charged sphere. Finally, the chapter concludes by explaining the visualization tools for the electrostatic field: field lines (vectors representing the field's direction and magnitude) and equipotential surfaces (surfaces of constant potential), noting that these two geometrical representations are always mutually perpendicular.