AP Physics C E&M: Gauss's Law

area vector, A

vector with magnitude equal to the area of a surface and direction perpendicular to the surface

cylindrical symmetry

system only varies with distance from the axis, not direction

electric flux, Φ

dot product of the electric field and the area through which it is passing

flux, Φ

quantity of something passing through a given area

free electrons

also called conduction electrons, these are the electrons in a conductor that are not bound to any
particular atom, and hence are free to move around

Gaussian surface

any enclosed (usually imaginary) surface

planar symmetry

system only varies with distance from a plane

spherical symmetry

system only varies with the distance from the origin, not in direction

Gauss's Law

The electric flux of the electric field through any closed surface (a Gaussian surface) is equal to the net charge
enclosed divided by the permittivity of free space.

perpendicular

The electric flux through a surface is proportional to the number of field lines crossing that surface. Note that this
means the magnitude is proportional to the portion of the field ___________ to the area.

flux, charge

Gauss's law relates the electric ___________ through a closed surface to the net ___________ within that surface.

symmetries

For a charge distribution with certain spatial ___________ (spherical, cylindrical, and planar), we can find a Gaussian
surface over which the magnitude of the electric field is constant over the surface. The electric field is then determined with Gauss's law.

zero, surface, perpendicular

The electric field inside a conductor that has reached electrostatic equilibrium is ___________. Any excess charge placed on a conductor resides entirely on the ___________ of the conductor. The electric field is ___________ to the surface of a conductor everywhere on that surface.