Chapter 2: Coulomb’s Law and Electric Fields — Vocabulary Flashcards

Vocabulary-style flashcards covering the key concepts, quantities, and relationships introduced in the Coulomb’s Law and Electric Field material.

Electric charge

Property of matter with two types (positive and negative); measured in Coulombs; smallest free unit is e (electron/proton); total charge is conserved.

Elementary charge (e)

Magnitude of charge on a proton or electron: e = 1.602×10^−19 C; charges are quantized in multiples of e.

Coulomb’s Law

Force between two point charges in vacuum: F = k_e q1 q2 / r^2 directed along the line joining the charges; F12 = −F21.

Coulomb constant (k_e)

k_e = 1/(4π ε0) ≈ 8.9875×10^9 N·m^2/C^2.

Permittivity of free space (ε0)

Electric constant: ε0 ≈ 8.854×10^−12 C^2/(N·m^2); relates to μ0 and c via ε0 μ0 c^2 = 1.

Permeability of free space (μ0)

μ0 = 4π×10^−7 N·s^2/C^2; related to ε0 and c by ε0 μ0 c^2 = 1.

Speed of light (c)

c = 299,792,458 m/s in vacuum; relates ε0 and μ0 via ε0 μ0 c^2 = 1.

Superposition principle (electrostatics)

Net electric force or field on a charge is the vector sum of forces/fields from all other charges.

Electric field (E)

Force per unit test charge: E = F/q0; created by charges; units N/C.

Test charge

Infinitesimally small charge used to probe an electric field without disturbing source charges.

Electric field due to a point charge

E = (1/(4π ε0)) (q r̂)/r^2; points away from positive charges and toward negative charges.

Electric field from multiple point charges

E = Σi (1/(4π ε0)) (qi r̂i)/ri^2; vector sum of individual fields.

Electric dipole

Two equal and opposite charges separated by distance; dipole moment p̂ points from −q to +q.

Dipole moment (p)

Magnitude p = q d (where d is separation); vector from negative to positive charge.

Electric field of a dipole (far field)

For r ≫ a, E = (1/(4π ε0)) [3(p·r̂)r̂ − p]/r^3; field falls as 1/r^3.

Torque on a dipole in a uniform field

τ = p × E; causes rotation to align p with the external field; direction given by right-hand rule.

Potential energy of a dipole in a uniform field

U(θ) = − p·E = − pE cosθ; minimum when p∥E (stable), maximum when antiparallel (unstable).

Non-uniform field force on a dipole

In a nonuniform field, a dipole experiences a net force F ≈ (p·∇)E (force due to field gradient).

Volume charge density (ρ)

ρ(r) = dq/dV; units: C/m^3; total charge Q = ∫ ρ dV.

Surface charge density (σ)

σ(r) = dq/dA; units: C/m^2; total charge on surface S: Q = ∬ σ dA.

Line charge density (λ)

λ = dq/dℓ; units: C/m; total charge on a line: Q = ∫ λ dℓ.

Electric field from a continuous distribution

E = ∫ (dq)/(4π ε0 r^2) r̂; total field is the vector integral of contributions from all dq.

Energy density of the electric field

u_E = (1/2) ε0 E^2; energy stored per unit volume in the electric field.

Discontinuity of E across a charged surface

Across a surface with surface charge σ, the normal component of E changes by ΔE_n = σ/ε0.

Charge conservation

Charge cannot be created or destroyed; total charge in a closed system remains constant.

Coulomb’s law and Newton’s third law

The force between two charges obeys F12 = −F21; action-reaction pair in electrostatics.

Point-dipole far-field fall-off

Electric field due to a dipole falls off as 1/r^3 in the far field (r ≫ separation).

Faraday’s lines of force

A graphical representation of the electric field lines showing the direction of the field and how forces are transmitted.

Point charge limit of a finite distribution

At distances large compared to the size, the field approaches that of a point charge with total charge Q.

Electric field on an infinite plane (surface charge)

For a plane with surface charge density σ, the field is perpendicular to the plane with magnitude E = σ/(2ε0) on each side; field discontinuity ΔE = σ/ε0.

Quantization of charge (Millikan concept)

Charge is quantized in integral multiples of e; demonstrated experimentally by oil-drop experiments.

Unit vector (r̂)

A dimensionless vector pointing from a source to the field point; used to specify direction of E and F.

Unit conventions for E and F directions

E and F point along field lines: E points in the direction a positive test charge would move; forces on charges follow Fe = qE.