AP Physics C Questions on Gauss's Law: Exam Preparation

📚 Quick Study Guide

• ⚛️ Gauss's Law relates the electric flux through a closed surface to the enclosed charge.
• 📝 The formula is: $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$, where $\vec{E}$ is the electric field, $d\vec{A}$ is the differential area vector, $Q_{enc}$ is the enclosed charge, and $\epsilon_0$ is the permittivity of free space ($\approx 8.854 \times 10^{-12} C^2/Nm^2$).
• 📏 Choose a Gaussian surface that takes advantage of the symmetry of the charge distribution (spherical, cylindrical, or planar).
• 💡 For spherical symmetry, use a spherical Gaussian surface. For cylindrical symmetry, use a cylindrical Gaussian surface. For planar symmetry, use a box-shaped Gaussian surface.
• ⚡️ Remember that $\vec{E}$ is constant and parallel to $d\vec{A}$ over the Gaussian surface you choose to simplify the integral.
• ➕ When calculating $Q_{enc}$, consider the charge density ($\rho$, $\sigma$, or $\lambda$) and the volume, area, or length enclosed by the Gaussian surface.
• 🎯 Key strategies: Identify symmetry, choose the appropriate Gaussian surface, calculate the electric flux, and solve for the electric field.

Practice Quiz

1. What does Gauss's Law relate?
1. Electric potential to the charge density.
2. Electric flux through a closed surface to the enclosed charge.
3. Electric field to the current density.
4. Magnetic field to the enclosed current.


2. What is the correct mathematical expression for Gauss's Law?
1. $\oint \vec{E} \cdot d\vec{A} = \mu_0 I_{enc}$
2. $\oint \vec{B} \cdot d\vec{A} = 0$
3. $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$
4. $\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt}$


3. For a spherically symmetric charge distribution, what shape should the Gaussian surface be?
1. Cube
2. Cylinder
3. Sphere
4. Plane


4. A point charge of +2q is placed at the center of a cube. What is the electric flux through one face of the cube?
1. $\frac{q}{6\epsilon_0}$
2. $\frac{q}{3\epsilon_0}$
3. $\frac{2q}{6\epsilon_0}$
4. $\frac{2q}{\epsilon_0}$


5. A long, straight wire has a uniform linear charge density $\lambda$. What Gaussian surface is most suitable to find the electric field at a distance r from the wire?
1. A sphere of radius r.
2. A cube with sides of length r.
3. A cylinder of radius r and length L.
4. A flat disc of radius r.


6. A large, flat, non-conducting sheet has a uniform charge density $\sigma$. The electric field near the surface of the sheet is:
1. $\frac{\sigma}{\epsilon_0}$
2. $\frac{\sigma}{2\epsilon_0}$
3. $\frac{\sigma}{4\pi\epsilon_0 r^2}$
4. 0


7. A solid conducting sphere of radius R has a total charge Q. What is the electric field inside the sphere (r < R)?
1. $\frac{kQ}{r^2}$
2. $\frac{kQr}{R^3}$
3. $\frac{kQ}{R^2}$
4. 0