Practice Test 7 - AP Physics C Electricity and Magnetism

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

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1. Consider the RC circuit shown: a capacitor initially at 10 V discharges through $R=4.7\times10^{3}\,\Omega$ with $C=4.7\times10^{-6}\,\text{F}$. What is the remaining voltage across the capacitor after discharging for 0.022 s?
2. Based on the provided data, which of the following conclusions is most justified?
3. A long, straight wire in vacuum carries $I=12\,\text{A}$ upward. Point $P$ lies $d=0.040\,\text{m}$ from the wire. Use the Biot-Savart result for an infinite wire: $B=\dfrac{\mu_0 I}{2\pi d}$ with $\mu_0=4\pi\times10^{-7}\,\text{T}\cdot\text{m/A}$. What is the magnitude of the magnetic field at point $P$ due to the wire?
4. In a diagram representing a magnetic field with field lines, what physical quantity corresponds to the density of the lines (how close they are to each other) in a given region?
5. Electric charge (C) is a conserved property that can be positive or negative; like charges repel and unlike charges attract. Electric force is the interaction between charges, directed along the line joining them. Two point charges in space are fixed: $q_1=-5.0\times10^{-6}\ \text{C}$ and $q_2=+2.0\times10^{-6}\ \text{C}$ separated by $r=0.50\ \text{m}$. Coulomb's Law gives $F=k\frac{|q_1q_2|}{r^2}=(8.99\times10^{9})\frac{|(-5.0\times10^{-6})(2.0\times10^{-6})|}{(0.50)^2}$. If additional charges were introduced, superposition would require adding all forces vectorially to find the net force on either charge. Calculate the force between two charges of $-5.0\ \mu\text{C}$ and $+2.0\ \mu\text{C}$, separated by $0.50\ \text{m}$.
6. A point charge $+q$ is fixed at the origin. An external force moves a second point charge $+Q$ from position A at ($r_0, 0$) to position B at ($0, r_0$). What is the work done by the electric field of the fixed charge during this displacement?
7. A transformer has $N_p=500$, $N_s=50$, and $V_p=120\ \text{V}_{\text{rms}}$; calculate induced secondary voltage magnitude.
8. A point charge $+Q$ is located at the origin. What is the electric flux through a spherical surface of radius $R$ centered at the origin?
9. In a particle-beam alignment rig, a thin insulating rod of length $L=0.40\ \text{m}$ lies along the $x$-axis from $x=-0.20$ m to $x=+0.20$ m with uniform linear charge density $\lambda=+6.0\ \mu\text{C/m}$. A sensor at point $P$ is on the perpendicular bisector at $y=0.30$ m. Consider the setup described above. Neglect end effects beyond the finite rod and use superposition to find the field at $P$ in N/C. Symmetry implies horizontal components cancel, leaving only a $+\hat{y}$ or $-\hat{y}$ direction depending on sign. The engineering goal is to predict sensor saturation during calibration.
10. A parallel-plate capacitor with charge $Q_0$ is fully discharged by connecting its terminals with a wire of resistance $R$. The total energy $U_0$ initially stored in the capacitor is dissipated as heat in the wire. If the same capacitor were instead charged to $3Q_0$, what would be the total energy dissipated in the wire during its discharge?
11. Which of the following correctly pairs a circuit component with its primary function in a simple circuit?
12. A transformer has $N_p=200$, $N_s=800$, and $V_p=24\ \text{V}_{\text{rms}}$; calculate induced secondary voltage magnitude.
13. A parallel-plate capacitor with capacitance $C$ is connected to a battery with a constant potential difference $V$. While the capacitor is connected to the battery, a dielectric slab with dielectric constant $\kappa$ is inserted between the plates. What is the magnitude of the work done by the battery during this process?
14. An ideal LC circuit contains an inductor of inductance $L$ and a capacitor of capacitance $C$. What is the period $T$ of the oscillations in this circuit?
15. An uncharged, isolated conducting sphere is placed in a pre-existing uniform external electric field that points to the right. After electrostatic equilibrium is reached, which statement best describes the electric field inside the sphere?
16. According to the scenario, a solenoid's current ramps up, increasing magnetic flux through a nearby coil; Faraday's Law $\mathcal{E}=-d\Phi/dt$ induces a current whose magnetic field opposes the increasing flux (Lenz's Law), as in transformer action. According to Faraday's Law, what happens to the induced EMF when the magnetic field changes?
17. A uniform electric field $E=8.0\times10^{2}\ \text{V/m}$ points upward. Point $B$ is $0.15\ \text{m}$ above point $A$. Use $\Delta V=-Ed$ along the field direction (and $k=8.99\times10^{9}$, $e=1.60\times10^{-19}\ \text{C}$). In the situation described, calculate the potential difference $V_B-V_A$.
18. Inductance is a property of an electrical conductor that measures its tendency to...
19. After the switch has been closed for a very long time (in the steady state), which equation correctly describes the circuit based on Kirchhoff's loop rule?

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