Practice Test 12 - 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. The mathematical statement $\oint \vec{B} \cdot d\vec{A} = 0$ is known as Gauss's law for magnetism. What is the fundamental physical principle that this law represents?
2. A positive test charge is placed at rest at point P in a region described by electric field lines. Assume only the electric force acts on the charge. Which statement best describes the initial motion of the charge?
3. A thin insulating spherical shell has total charge $Q=+4.0\,\text{nC}$ uniformly spread over its surface. Using Gauss's Law with a spherical Gaussian surface of radius $r=0.20\,\text{m}$ centered on the shell, charge is conserved and symmetry makes $E$ constant on the surface. Based on Gauss's Law, what is the electric flux through the Gaussian surface?
4. What is the electric potential of the inner shell at radius $R_1$? Assume the potential is zero at an infinite distance.
5. A hollow cylindrical conductor has an inner radius of $R_1$ and an outer radius of $R_2$. A steady current $I$ flows along the conductor, distributed uniformly over its cross-section. What is the magnitude of the current density $J$ within the conductor?
6. What is the equivalent resistance of this entire network of resistors?
7. A uniform electric field of magnitude $E=2.50\times10^{3}\ \text{V/m}$ points in the $+x$ direction between large parallel plates. Points $A$ and $B$ are separated by $d=0.040\ \text{m}$ along $+x$. Use $\Delta V=-Ed$ (and $k=8.99\times10^{9}$, $e=1.60\times10^{-19}\ \text{C}$). Based on the data, calculate the potential difference $V_B-V_A$.
8. A parallel-plate capacitor is connected to a battery with a constant potential difference $V_0$. While connected, the area of the plates that directly overlaps is decreased by a factor of two. What is the ratio of the final stored energy to the initial stored energy?
9. The energy stored in the electric field of a charged system can be calculated by integrating the energy density $u_E = \frac{1}{2} \epsilon_0 E^2$ over all space. For an isolated conducting sphere of radius $R$ and charge $Q$, the electric field for $r > R$ is $E = \frac{Q}{4\pi\epsilon_0 r^2}$. Which integral correctly calculates the energy stored in the field outside the sphere?
10. A battery with emf $\varepsilon=18\,\text{V}$ and internal resistance $r=2.0\,\Omega$ is connected to an external load resistor $R=7.0\,\Omega$ in series (single loop). Using Kirchhoff's Loop Rule, what is the potential difference across the battery terminals while delivering current to the load?
11. An electric dipole, consisting of charges $+q$ and $-q$ separated by a small distance, is placed in a uniform external electric field. Which statement correctly describes the net force and net torque on the dipole?
12. A solid, isolated conducting sphere is given a net negative charge. Once the sphere reaches electrostatic equilibrium, where is the excess charge located?
13. Solve for the unknown current $I_3$ entering junction C if $I_1=1.20\,\text{A}$ and $I_2=0.45\,\text{A}$ leave junction C, and $I_4=0.30\,\text{A}$ enters.
14. The susceptibility $χ_e$ of a dielectric material is defined by the relation $κ = 1 + χ_e$. What does the electric susceptibility physically represent?
15. A steady current flows through a conical conductor of uniform resistivity. The conductor's circular cross-section has a radius that increases linearly from left to right. How does the drift velocity of the charge carriers vary along the length of the conductor from left to right?
16. In a series $R$–$L$ loop, Kirchhoff gives $V- iR - L\,di/dt=0$; induced emf opposes change; Refer to the scenario above. Explain the significance of Lenz's Law in the scenario provided.
17. A conducting sphere of radius $R_1$ holds charge $Q_1$. A concentric conducting shell of inner radius $R_2$ and outer radius $R_3$ holds charge $Q_2$. The sphere and shell are connected by a wire. What is the final charge on the inner sphere?
18. Which of the following best describes why Ampère's law is particularly useful for calculating magnetic fields in highly symmetric current distributions?
19. Two isolated conducting spheres, Sphere 1 with radius $R$ and Sphere 2 with radius $2R$, are located far apart. Sphere 1 has charge $+Q$ and Sphere 2 is uncharged. They are then connected by a long, thin conducting wire. After the system reaches electrostatic equilibrium, which statement is correct?
20. A rectangular loop of wire enters a region of uniform magnetic field at a constant speed $v$, resulting in a magnetic braking force $F$. If the experiment is repeated with a new loop made of a wire with twice the resistivity but otherwise identical dimensions, moving at the same speed $v$, what will be the new braking force?

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