Electricity starts with charge and the forces between charges. This unit turns those forces into fields, builds the fields of continuous charge distributions with integrals, and then trades the integrals for symmetry using Gauss's law, the first of Maxwell's equations.
Charge is a scalar, positive or negative, in multiples of e. Coulomb's law: the force between point charges is proportional to each charge and to 1/r², along the line between them; like charges repel, opposites attract. Electric forces dwarf gravity between particles. Permittivity measures how a material polarizes; conductors let charge move, insulators don't.
A system's net charge changes only if charge (usually electrons) is transferred in or out, by friction or contact. Nearby charges can polarize even a neutral object (induced charge separation). Grounding connects an object to a huge neutral reservoir like Earth.
The electric field is force per unit test charge, E = F/q. It points away from positive and toward negative charges; fields from several charges add as vectors. In electrostatic equilibrium a conductor's excess charge sits on its surface, the field inside is zero, and the field at the surface is perpendicular to it.
For continuous charge, add up the fields of tiny pieces: dE = k dq/r², integrated with superposition, using symmetry to cancel components. The exam limits this to an infinite line or cylinder, a ring on its axis, a semicircular arc at its center and a finite line on its axis or perpendicular bisector.
Electric flux measures field through an area: Φ = E·A for uniform E, or a surface integral. Gauss's law says the total flux through a closed surface equals the enclosed charge over ε₀, regardless of the surface's size. With spherical, cylindrical or planar symmetry it gives E directly. It is the first of Maxwell's equations.