Flux and Gauss’ Law lecture notes

A set of vocabulary flashcards covering the concepts of electric flux, Gauss's Law, charge distribution, and conductor properties based on lecture notes from September 26, 2007.

Flux ($q$) in Physics

Refers to the rate of flow (e.g., volume per unit area per unit time for water) or the amount of energy per unit area per unit time (for light).

Area Vector

An representation of an area as a vector with a length equal to the area and a direction of the outward normal to the surface.

$\Phi$ (Greek letter phi)

The symbol used to represent the flux of the electric field through an element of area.

Positive Electric Flux

The condition occurring when the angle $\theta < 90^\circ$, indicating the flux is moving out of the surface.

Negative Electric Flux

The condition occurring when the angle $\theta > 90^\circ$, indicating the flux is moving into the surface.

Gaussian surface

A closed surface over which the electric flux is integrated, as used in Gauss’ Law.

Gauss’ Law

States that the flux of the electric field through a closed surface is proportional to the charge enclosed ($q_{enc}$).

$$\epsilon_0$$

The constant of proportionality in Gauss’ Law.

Electric Field inside a Conductor

The electric field is zero inside because charges move to nullify any parallel component of $E$; consequently, all net charge resides on the surface.

Charge Distribution on Conductors

Charges spread evenly on a conducting sphere but tend to collect near sharp curvature on other shapes.

Induced Charge in a Cavity

A charge placed inside a conductor's cavity induces an equal and opposite charge on the inner surface of that cavity.

Surface charge density ($\sigma$)

For plate or plane geometry, it is defined as total charge $Q$ divided by the total area $A_{tot}$ ($\sigma = \frac{Q}{A_{tot}}$).

Linear charge density ($\lambda$)

For line geometry, it is defined as total charge $Q$ divided by the total length $L_{tot}$ ($\lambda = \frac{Q}{L_{tot}}$).

Volume charge density ($\rho$)

For spherical geometry where charges are distributed throughout the volume, it is defined as total charge $Q$ divided by volume $V$ ($\rho = \frac{Q}{V}$).

Field at the Surface of a Conductor

The electric field is always perpendicular (normal) to the surface because parallel components are nullified by the movement of free charges.

Nonconducting Sheet Flux

Unlike a conducting plate, flux exists out of both ends of the gaussian surface because one end cannot close inside a conductor, resulting in a field half as strong as a conducting plate.

Principle of superposition

Used to calculate the internal electric field between two nonconducting sheets by adding the individual fields, which results in a field twice as strong as a single sheet.