The foundation of electrostatics — how charge behaves, why Coulomb's Law works the way it does, and how the electric field lets us describe force without contact.
Electric charge is a basic property of matter, alongside mass, that determines how a particle interacts electrically and magnetically with everything around it. Rub a glass rod with silk, or a plastic comb through dry hair, and you can pick up small bits of paper — that's charge in action, first noticed in ancient Greece with amber ("elektron"), which is where the word "electricity" comes from.
Benjamin Franklin named the two kinds of charge positive and negative. Charge on a glass rod rubbed with silk is called positive; charge on a plastic rod rubbed with fur is called negative. The rule that follows from experiment:
Materials differ in how easily charge moves through them. In conductors (metals, the human body, earth), electrons move relatively freely, so charge given at one point spreads over the surface almost instantly. In insulators (glass, rubber, most plastics), charge stays localized where it's placed, since electrons are tightly bound to atoms.
You can charge a conductor without touching it: bring a charged rod near an uncharged conductor, and charges within the conductor redistribute — opposite charge accumulates on the near side, like charge on the far side. Ground the far side momentarily and disconnect, and the conductor is left with a net charge opposite to the rod's — without ever transferring charge directly.
Charges add up like real numbers — if a system has charges q₁, q₂, q₃, ... at different points, the total charge is simply their algebraic sum, taking sign into account.
The total charge of an isolated system never changes. Charge isn't created or destroyed — it's only transferred from one body to another. When you rub glass with silk, the glass doesn't gain charge from nowhere; electrons move from glass to silk (or vice versa), so the combined charge of both stays exactly zero, same as before.
Charge doesn't come in arbitrary amounts — it always exists as an integer multiple of a smallest unit, the charge of an electron.
Coulomb's Law gives the force between two point charges at rest, separated by some distance. It's the electrostatic equivalent of Newton's law of gravitation, and it's the starting point for almost everything else in this chapter.
In vector form, the force on charge q₁ due to q₂, at position vectors r₁ and r₂, is written using the unit vector r̂₂₁ pointing from q₂ to q₁:
When more than two charges are present, the net force on any one charge is simply the vector sum of the forces due to each of the other charges individually, as if the others weren't there. This is the superposition principle, and it's what makes electrostatics tractable — you can always break a complicated arrangement down into pairwise Coulomb forces and add them as vectors.
Rather than tracking forces between every possible pair of charges, it's more useful to ask: what does a charge do to the space around it? The answer is the electric field — a vector quantity defined at every point in space, describing the force a small positive "test charge" would feel if placed there.
The field due to a single point charge Q at distance r follows directly from Coulomb's Law:
Field lines are a way to visualize E — imaginary curves drawn so the tangent at any point gives the field's direction there, and the density of lines indicates field strength.
An electric dipole is a pair of equal and opposite charges (+q and −q) separated by a small distance 2a. Dipoles matter well beyond textbook problems — polar molecules like water behave as tiny electric dipoles, which is central to a lot of chemistry and biology.
Along the line through both charges, extended outward, for a point far from the dipole (r ≫ a):
Along the perpendicular bisector of the dipole, for r ≫ a:
A uniform field exerts no net force on a dipole (the forces on +q and −q are equal and opposite), but it does exert a torque that tries to align the dipole with the field:
Electric flux is a measure of how much field "passes through" a given surface — think of it loosely as counting field lines crossing an area.
Gauss's Law connects the electric flux through any closed surface to the total charge enclosed by it — and it's exact, not an approximation, following directly from Coulomb's Law.
Two point charges, +3 μC and −3 μC, are placed 30 cm apart in air. Find the force between them.
Solution: F = kq₁q₂/r² = (9×10⁹ × 3×10⁻⁶ × 3×10⁻⁶) / (0.3)² = (8.1×10⁻²) / (0.09) = 0.9 N.
Since the charges are unlike, the force is attractive, directed along the line joining them.
A dipole with moment p = 4×10⁻⁹ C·m is placed at a point 0.1 m from its centre on the equatorial line. Find the electric field there.
Solution: E = kp/r³ = (9×10⁹ × 4×10⁻⁹) / (0.1)³ = 36 / 0.001 = 3.6×10⁴ N/C, directed opposite to p.