Foundations of Electrostatics: Charge, Coulomb Interaction, and Realistic Charge Distributions

Electric charge

A fundamental property of matter that causes electric interactions; like charges repel and unlike charges attract (charge is the “source” of electric forces/fields).

Charge conservation

Principle that the total charge of an isolated system remains constant: if no charge enters/leaves, then Qinitial = Qfinal (charge can be transferred between objects, but total stays fixed).

Elementary charge (e)

The fundamental unit of charge magnitude: e = 1.602×10^−19 C (protons have +e, electrons have −e).

Quantization of charge

Charge exists in discrete amounts; any net charge is an integer multiple of e: q = n e, where n is an integer.

Conductor

Material in which charges (typically electrons) move freely; excess charge redistributes and, at electrostatic equilibrium, resides on the surface.

Insulator

Material in which charges are bound to atoms/molecules and do not move freely through the object.

Polarization

Slight separation/shift of positive and negative charge within a neutral object (e.g., molecular distortion in insulators or electron movement in conductors), enabling attraction to a nearby charged object without changing net charge.

Electrostatic equilibrium (conductor)

State where charge on a conductor has finished redistributing; in this state, excess charge is on the surface (not throughout the volume).

Charging by friction (triboelectric effect)

Charging process where rubbing transfers electrons between materials; one object gains electrons (becomes negative) and the other loses electrons (becomes positive).

Charging by conduction (contact)

Charging process where a charged conductor touches another conductor and charge flows until they reach the same electric potential; total charge is conserved.

Charging by induction

Charging without contact: a nearby charge rearranges charges in a conductor; with a grounding step and proper removal sequence, the conductor can end with a net charge.

Grounding

Providing a conducting path to Earth so electrons can flow to/from an object during induction, depending on whether the external charge attracts or repels electrons.

Coulomb’s law

Law giving the electrostatic force between two point charges at rest: magnitude F = k |q1 q2| / r^2, along the line joining the charges.

Coulomb’s constant (k)

Constant in Coulomb’s law: k = 1/(4π ε0) ≈ 8.99×10^9 N·m^2/C^2.

Permittivity of free space (ε0)

Physical constant relating to electric interactions in vacuum: ε0 = 8.854×10^−12 C^2/(N·m^2).

Point charge

Idealized charge whose size is negligible compared with the distances involved, allowing it to be treated as located at a single point.

Inverse-square dependence

Relationship where a force magnitude decreases as 1/r^2; in Coulomb’s law, doubling r makes the force 1/4 as large.

Vector form of Coulomb force

Force on q1 due to q2 written with direction explicitly: F⃗{1←2} = k (q1 q2 / r^2) r̂{1←2}, where the sign of q1 q2 sets attraction vs. repulsion.

Unit vector r̂_{1←2}

A unit vector pointing from charge q2 toward charge q1; used to encode direction in Coulomb’s law vector form.

Superposition principle (electric force)

Net electrostatic force on a charge equals the vector sum of forces from all other charges: F⃗net = Σ F⃗{←i}.

Charge distribution

Model where charge is spread continuously over an object (line/surface/volume); you divide into small pieces dq and integrate their Coulomb-law contributions.

Differential charge element (dq)

An infinitesimal piece of charge used in integrals for distributions; typically dq = λ dl, dq = σ dA, or dq = ρ dV.

Linear charge density (λ)

Charge per unit length along a line/rod: λ = dq/dl (units: C/m). For uniform density, λ = Q/L.

Surface charge density (σ)

Charge per unit area on a surface: σ = dq/dA (units: C/m^2).

Volume charge density (ρ)

Charge per unit volume in a region: ρ = dq/dV (units: C/m^3).