Practice Test 10 - AP Physics C Electricity and Magnetism

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. After the system reaches electrostatic equilibrium, where will the majority of the positive charge reside?
2. In an ideal LC circuit with inductance $L = 4.0$ H and capacitance $C = 9.0$ F, the maximum current observed is $I_{max} = 0.5$ A. What is the maximum charge $Q_{max}$ stored on the capacitor?
3. A uniform electric field is given by $\vec{E} = (200 \hat{i} - 300 \hat{j}) \text{ N/C}$. What is the electric flux through a flat rectangular surface of area $0.5 \text{ m}^2$ lying in the xz-plane?
4. Circuit A consists of an inductor $L$ and a resistor $R$. Circuit B consists of an inductor $2L$ and a resistor $R/2$. Both are connected to identical batteries at $t=0$. How does the final steady-state current $I_A$ in circuit A compare to $I_B$ in circuit B, and how does the time constant $\tau_A$ compare to $\tau_B$?
5. The current $I$ through a circuit component is measured as a function of the potential difference $V$ across it. A plot of $I$ as a function of $V$ is a straight line passing through the origin with a slope of $0.05\,\text{A/V}$. What is the resistance of the component?
6. What is the final charge distribution on the sphere?
7. A solid circular conducting disk is moving at a constant velocity into a uniform magnetic field directed into the page. Eddy currents are induced in the disk. Which statement correctly describes the net magnetic force on the disk due to these eddy currents?
8. A very large, thin, nonconducting sheet has a uniform positive surface charge density $\sigma$. What is the magnitude of the electric field at a point near the center of the sheet?
9. A $+6.0\,\mu\text{C}$ rod touches a neutral metal sphere on an insulating stand; after separation, what is the sphere's charge?
10. A rectangular current loop (dimensions $0.10\,\text{m}\times0.20\,\text{m}$) carries current $I=2.0\,\text{A}$, meaning charges move around the loop and create a magnetic dipole moment $\vec\mu=IA\,\hat n$. The loop is in a uniform magnetic field $\vec B=0.30\,\text{T}$ to the right. The torque on the loop is $\vec\tau=\vec\mu\times\vec B$; equilibrium occurs when $\vec\mu$ is parallel or antiparallel to $\vec B$. Refer to the scenario above. Determine the net force on the loop in the uniform magnetic field.
11. A nearby solenoid current increases at $dI/dt=3.0\ \text{A/s}$; a loop has mutual inductance $M=0.040\ \text{H}$; induced EMF magnitude?
12. A uniform magnetic field is given by the vector $\vec{B} = (4.0 \hat{i} - 3.0 \hat{j})$ T. A flat, square surface with side length $2.0$ m lies in the yz-plane. What is the magnetic flux through this surface?
13. A precision ion trap uses a uniformly charged thin ring (insulating) of radius $R=0.12\ \text{m}$ carrying total charge $Q=+3.0\ \text{nC}$. A test point $P$ lies on the ring's axis a distance $z=0.09\ \text{m}$ from the center. Consider the setup described above. The field is needed to estimate the axial restoring force on ions near the center. Use the standard on-axis ring result and give direction along $\pm\hat{z}$ in N/C.
14. A parallel-plate capacitor creates a uniform electric field of magnitude $E$ in the volume between its plates. The permittivity of free space is $\epsilon_0$. What is the energy density, or energy stored per unit volume, in the electric field?
15. Two spherical conductors have radii $r_1$ and $r_2$ and initial charges $q_1$ and $q_2$. They are connected by a conducting wire. In which direction will charge flow?
16. A point charge $+Q$ is located at the center of a spherical Gaussian surface of radius $R$. The net electric flux through the surface is $\Phi_E$. If the radius of the sphere is doubled to $2R$ while the enclosed charge remains at the center, what is the new net electric flux?
17. A thin ring of radius $R$ holds a total charge $+Q$ distributed uniformly. The magnitude of the electric field along the central axis is given by $E(z) = \frac{kQz}{(z^2 + R^2)^{3/2}}$, where $z$ is the distance from the center of the ring. At what distance $z$ from the center is the magnitude of the electric field at its maximum value?
18. A circular loop ($A=0.010\ \text{m}^2$) in $B=0.40\ \text{T}$ has its normal rotate from $0^\circ$ to $60^\circ$; determine flux change.
19. A sensitive electronic component must be protected from stray external static electric fields. What is the most effective method for shielding it?
20. Ampère's law relates the circulation of the magnetic field around a closed path to which of the following quantities?

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