Gauss's Law and Electric Flux - Lecture Notes Review

Flashcards covering Gauss's Law, electric flux, surface integrals, and symmetry concepts from the lecture notes on Gauss's Law (Ch. 24).

What is Gauss's law in its basic form?

The electric flux through a closed surface equals the enclosed charge divided by ε0 (Φ = Q_enclosed/ε0).

How is electric flux Φ defined for a uniform field through a surface?

Φ = E · A = E A cos θ, where θ is the angle between E and the surface normal.

What is a Gaussian surface?

A closed surface used to apply Gauss's law to relate flux to enclosed charge.

What is a surface integral in the context of electric flux?

An integral of E · dA over a surface, used when the electric field is nonuniform.

What does the vector dA represent in flux calculations?

An infinitesimal area vector perpendicular to the surface element, with magnitude equal to the element's area.

How is the flux through a curved surface calculated?

Φ = ∮ E · dA over the curved surface, i.e., the sum of fluxes through all differential area elements.

What is the flux through a closed surface that encloses no net charge?

Zero (the net flux is zero if no net charge is enclosed).

What is Qin in Gauss's law?

The sum of all charges inside the Gaussian surface.

What is the flux through any closed surface around a point charge q?

Φ = q/ε0, independent of the surface shape or size.

What is the field outside a sphere with total charge Q?

Outside, the field is as if a point charge Q were at the center: E = kQ/r^2.

If two spherical Gaussian surfaces enclose the same total charge, which has larger flux?

They have the same flux; flux depends only on the enclosed charge.

For what situations is Gauss's law especially useful?

Calculating electric fields for highly symmetric charge distributions (planar, cylindrical, spherical symmetry).

Is Gauss's law applicable to moving charges?

Yes; Gauss's law is valid for moving charges, whereas Coulomb's law is not always directly applicable.

What is the relationship between flux and radius for a point charge?

The flux through any closed surface around a point charge is Φ = q/ε0, independent of the radius.

What does Gauss's law say about the external field of a charged sphere?

Outside the sphere, the field is the same as that of a point charge at the center (E = kQ/r^2).

What is a key takeaway about electric flux through closed surfaces around a point charge?

Flux depends only on the enclosed charge and not on the specific shape or size of the surface.