1. Choose a Gaussian surface. 2. Calculate the electric flux through the surface. 3. Determine the enclosed charge. 4. Apply Gauss's Law to solve for the electric field.

1. Choose a spherical Gaussian surface. 2. Calculate flux: $\Phi = E(4\pi r^2)$. 3. Find enclosed charge. 4. Apply Gauss's Law: $E = \frac{Q_{enc}}{4\pi \epsilon_0 r^2}$.

1. Define the area vector. 2. Determine the electric field vector. 3. Calculate the dot product: $\Phi = \vec{E} \cdot \vec{A} = EA \cos(\theta)$.

1. Define the volume element $dV$. 2. Express charge density as function of position $\rho(r)$. 3. Integrate: $q_{enc} = \int \rho(r) dV$.

1. Define the path of integration. 2. Calculate the line integral: $V(r) = - \int_{\infty}^{r} \vec{E} \cdot d\vec{r}$.

1. Count electric field lines entering. 2. Count electric field lines exiting. 3. If entering = exiting, net flux = 0.

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

Entering: Negative flux. | Exiting: Positive flux.

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

Electric flux: Measure of field lines through an area. | Electric field: Force per unit charge at a point.

Spherical: Use spherical Gaussian surface, $A = 4\pi r^2$. | Cylindrical: Use cylindrical Gaussian surface, $A = 2\pi r L$.

1: Electric Field Lines, 2: Area Vector, 3: Angle $\theta$

1: Lines Entering (Negative Flux), 2: Lines Exiting (Positive Flux)

1: Electric Flux ($\Phi_E$), 2: Surface Integral ($\oint \vec{E} \cdot d\vec{A}$), 3: Enclosed Charge ($Q_{enc}$), 4: Permittivity of Free Space ($\epsilon_0$)

1: Gaussian Surface, 2: Radius (r), 3: Charge (Q)

1: Spherical Charge Distribution, 2: Gaussian Surface, 3: Electric Field (E)