Electrostatics: Electric Flux and Gauss's Law

Vocabulary flashcards covering the concepts, equations, and conventions of electric flux over open and closed surfaces and the initial derivation steps for Gauss's law.

Total Electric Flux for an Entire Surface

The surface integral obtained by taking the limit $\Delta A_i \rightarrow 0$ of the summation of discrete areal flux contributions, which depends on both the electric field pattern on the surface area and the orientation of the surface with respect to the electric field.

Direction of $d\mathbf{A}$ (Closed Surface)

The outward normal vector defined for each areal element on a closed surface.

Total Electric Flux over a Closed Surface

The closed surface integral given by $\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A}$, which can have a value that is negative, positive, or zero.

Positive Electric Flux (Closed Surface)

The condition occurring over an area element when the angle between $d\mathbf{A}$ and $\mathbf{E}$ is less than $90^\circ$, indicating that the electric field lines leave the closed surface.

Negative Electric Flux (Closed Surface)

The condition occurring over an area element when the angle between $d\mathbf{A}$ and $\mathbf{E}$ is greater than $90^\circ$, indicating that the electric field lines enter the closed surface.

Electric Field of a Positive Point Charge

A field directed radially outward at all points on an imaginary spherical surface of radius $r$ surrounding the positive charge $Q$, making the angle $\theta = 0^\circ$ between the area element $d\mathbf{A}$ and $\mathbf{E}$.

Flux through a Spherical Surface enclosing a Charge $Q$

The total electric flux evaluated as $\Phi_E = \oint E\,dA$, derived from $\oint E\,dA\,\cos(\theta)$ where $\cos(0^\circ) = 1$.