Gauss' Law and Applications (Review & Summary)

A set of vocabulary flashcards covering Gauss's Law, Coulomb's Law, and the classic results for conductors, lines, sheets, and spherical charges.

Gauss's Law

The net electric flux through any closed surface equals the enclosed charge divided by ε0: \oint E\cdot dA=\frac{q_{_{}enclosed}}{\varepsilon_0}

Electric flux

ΦE, the amount of electric field crossing a surface, given by ΦE = ∮ E · dA.

Gaussian surface

An imaginary closed surface used to apply Gauss's Law and exploit symmetry in electrostatics.

Charge enclosed

q_enclosed, the net charge contained inside a Gaussian surface.

Net flux

The total flux through a closed surface, equal to ∮ E · dA.

Coulomb's law

Description of the force between point charges; F = k q1 q2 / r^2; E = F/q; k = 1/(4π ε0). Coulomb's law can be derived from Gauss's Law.

Conducting surface

A surface of a conductor; in electrostatic equilibrium, excess charge resides on the outer surface.

E outside a conductor

The electric field just outside a charged conducting surface is perpendicular to the surface with magnitude E = σ/ε0 (n̂ direction outward for positive σ).

E inside a conductor

Inside a perfect conductor, the electric field E = 0 in electrostatic equilibrium.

Infinite line of charge

A straight line with uniform linear charge density λ, producing E = λ/(2π ε0 r) radially outward from the line.

Linear charge density

λ, the amount of charge per unit length along a line.

Infinite sheet of charge

An infinite plane with uniform surface charge density σ, producing E = σ/(2ε0) on each side, perpendicular to the sheet.

Surface charge density

σ, the amount of charge per unit area on a surface.

Spherical shell of charge

A thin spherical shell of radius R with total charge q; external field behaves as if all charge is at the center; internal field is zero for r < R.

Exterior field of a spherical shell

For r ≥ R, E(r) = (1/(4π ε0)) q / r^2, directed radially.

Interior field of a spherical shell

For r < R, E(r) = 0 (field inside a thin spherical shell).

Uniform solid sphere of charge

A solid sphere with uniform volume charge density ρ; inside field E = (ρ r)/(3 ε0) ; outside E = (1/(4π ε0)) Q / r^2 .