Gauss's Law and Electric Flux (Video Notes)

30 vocabulary flashcards covering Gauss's law, Gaussian surfaces, electric flux, and the infinite sheet scenario from the notes.

Gauss's law

The total electric flux through a closed surface equals the enclosed charge divided by the vacuum permittivity, φ_E = q/ε0.

Gaussian surface

An imagined closed surface used in Gauss's law to enclose charge and calculate flux.

Electric flux

The amount of electric field passing through a given area; a scalar quantity, φ_E.

Permittivity of free space

The constant ε0 that relates electric field and flux; ε0 = 1/(4πk).

Vacuum permittivity

Another name for the permittivity of free space, ε0.

Coulomb constant

The constant k in Coulomb's law; ε0 = 1/(4πk).

ε0 = 1/(4πk)

Relation between vacuum permittivity and Coulomb constant.

Total charge enclosed

The charge contained within the Gaussian surface (q).

Surface charge density

The amount of charge per unit area on a surface (σ).

Surface area

The area over which flux is calculated (A).

Electric field

The vector field E representing the force per unit charge on a test charge.

Infinite sheet of charge

An idealized plane of charge extending without bound, producing a uniform electric field.

Electric field of an infinite sheet

For an infinite sheet, E = σ/(2ε0); the field is uniform and perpendicular to the sheet.

Cylinder as Gaussian surface

A cylindrical closed surface used to exploit symmetry when analyzing a sheet of charge.

Flux through the top surface

The flux through the top face of the cylinder; equals E*A since the field is perpendicular.

Flux through the bottom surface

The flux through the bottom face of the cylinder; equals E*A and has opposite orientation to the top.

Flux through the side surface

Flux through the cylindrical side; zero because E is parallel to the side.

Equal top and bottom flux

Top and bottom contributions are equal in magnitude due to symmetry of the sheet.

Orientation relative to field

Flux depends on how the surface is oriented relative to the electric field; parallel surfaces yield little or no flux.

Field independence of position

For an infinite sheet, the electric field has the same magnitude everywhere.

Inverse-square law

The electric field from a point charge decreases as 1/r^2, unlike the sheet case with a constant field.

Symmetry in choosing Gaussian surface

Choose a surface shape that makes the area calculation easy by exploiting symmetry.

q = σA

Charge on a patch of area A of a sheet equals surface density times area.

E = σ/(2ε0)

Electric field magnitude due to an infinite sheet of charge.

Flux equals E*A

For a surface perpendicular to E, the flux through that surface is E times the area.

Flux through a closed surface

Total flux through a closed surface equals q/ε0.

Electric flux is a scalar

Flux has magnitude but no direction.

Bucket flux analogy

An analogy illustrating how flux depends on area orientation and opening, like rain through a bucket.

Flux and field strength relationship

Flux increases with greater field strength and larger surface area.

Utility of Gauss's law

Allows finding E for symmetric charge distributions without tracking every particle interaction.

Flux through the top and bottom surfaces are equal

Because the sheet is symmetric, top and bottom flux magnitudes are equal.

Flux through the side surface is zero due to orientation

The field is parallel to the side, so no flux passes through it.

Charge density is constant for the sheet segment

σ is uniform, so q = σA applies to any patch of the sheet.