A measure of the electric field passing through a given surface.

The total electric flux through a closed surface is directly proportional to the total charge enclosed by that surface.

An imaginary, closed 3D surface used to apply Gauss's Law.

Charge per unit length, expressed as $Q_{\text {total }}=\int \lambda(x) dx$.

Charge per unit area, expressed as $Q_{\text {total }}=\int \sigma(x, y) dA$.

Charge per unit volume, expressed as $Q_{\text {total }}=\int \rho(\vec{r}) dV$.

Electric Fields: $\oint \vec{E} \cdot d \vec{A}= \frac{q_{\text{enc}}}{\varepsilon_{0}}$ (relates flux to enclosed charge) | Magnetic Fields: $\oint \vec{B} \cdot d \vec{A}=0$ (magnetic flux through any closed surface is always zero).

1. Identify the symmetry of the charge distribution. 2. Choose an appropriate Gaussian surface. 3. Calculate the electric flux through the Gaussian surface. 4. Calculate the enclosed charge. 5. Apply Gauss's Law to solve for the electric field.

Integrate the linear charge density function $\lambda(x)$ over the length of the charge distribution: $Q_{\text {total }}=\int \lambda(x) dx$.

Integrate the surface charge density function $\sigma(x, y)$ over the area of the charge distribution: $Q_{\text {total }}=\int \sigma(x, y) dA$.

Integrate the volume charge density function $\rho(\vec{r})$ over the volume of the charge distribution: $Q_{\text {total }}=\int \rho(\vec{r}) dV$.