What is the effect of enclosing more charge within a Gaussian surface?
The electric flux through the surface increases proportionally.
What happens if the electric field is parallel to the Gaussian surface?
The electric flux through that portion of the surface is zero.
What happens if the electric field is perpendicular to the Gaussian surface?
The dot product $\vec{E} \cdot d \vec{A}$ simplifies to $E dA$, making the integral easier to solve.
What is the effect of choosing a Gaussian surface that matches the symmetry of the charge distribution?
It simplifies the integral in Gauss's Law, making the calculation of the electric field easier.
What are the differences between Gauss's Law for Electric Fields and Gauss's Law for Magnetic Fields?
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).
What is electric flux ($Phi_E$)?
A measure of the electric field passing through a given surface.
What is Gauss's Law?
The total electric flux through a closed surface is directly proportional to the total charge enclosed by that surface.
What is a Gaussian surface?
An imaginary, closed 3D surface used to apply Gauss's Law.
What is linear charge density ($lambda$)?
Charge per unit length, expressed as $Q_{\text {total }}=\int \lambda(x) dx$.
What is surface charge density ($sigma$)?
Charge per unit area, expressed as $Q_{\text {total }}=\int \sigma(x, y) dA$.
What is volume charge density ($\rho$)?
Charge per unit volume, expressed as $Q_{\text {total }}=\int \rho(\vec{r}) dV$.
