The measure of how much of an electric field passes through a given area.

The electric flux through a closed surface is proportional to the enclosed charge.

An imaginary closed surface used to apply Gauss's Law, chosen to simplify the calculation of electric flux.

The permittivity of free space, a physical constant.

A charge distribution where the charge is evenly distributed throughout a volume or surface.

A charge distribution where the charge density varies with position.

Positive flux: Field lines exiting a closed surface. Negative flux: Field lines entering a closed surface.

Uniform: Charge is evenly distributed. Non-uniform: Charge density varies with position.

Conductors: Electric field inside is always zero. Insulators: Electric field can exist inside.

Electric Flux: Measure of the 'flow' of the electric field through a given area. Electric Field: Force per unit charge at a given point.

Sphere: Gaussian surface is a sphere. Cylinder: Gaussian surface is a cylinder. Different surface area calculations are required.

1. Choose a Gaussian surface. 2. Calculate the electric flux through the surface. 3. Determine the enclosed charge. 4. Apply Gauss's Law: $\Phi_E = \frac{Q_{enc}}{\epsilon_0}$.

1. Identify the electric field $E$. 2. Identify the area $A$. 3. Calculate $\Phi = EA$.

1. Identify the electric field $E$. 2. Identify the area $A$. 3. Identify the angle $\theta$ between $E$ and $A$. 4. Calculate $\Phi = \vec{E} \cdot \vec{A} = EA \cos(\theta)$.

1. Choose a spherical Gaussian surface. 2. Calculate the flux: $\Phi = E(4\pi r^2)$. 3. Determine the enclosed charge $Q_{enc}$. 4. Apply Gauss's Law to find $E$.

1. Define the volume element $dV$. 2. Set up the integral: $q_{enc} = \int \rho(r) dV$. 3. Evaluate the integral to find $q_{enc}$.