Practice Test 9 - 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. A capacitor with capacitance $C$ is charged to a potential difference $V$, storing an amount of energy $U$. If the potential difference is increased to $3V$, what is the new amount of energy stored in the capacitor?
2. Considering the information provided, a lightbulb in a household circuit follows Ohm's Law $V=IR$, where $R$ (in $\Omega$) limits $I$ (in A). Resistivity $\rho$ (in $\Omega\cdot\text{m}$) is a material property affecting $R$. What happens to current if resistance increases and voltage remains constant according to $V=IR$?
3. A long cylindrical capacitor has an inner conductor of radius $a$ and an outer conductor of radius $b$. The inner conductor holds a charge per unit length of $+\lambda$. The electric field in the region $a < r < b$ is given by $E = \frac{\lambda}{2\pi\epsilon_0 r}$. What is the magnitude of the potential difference between the conductors?
4. What is the approximate current in the circuit at time $t = 0.40$ s?
5. A toroidal inductor in air has $N=300$ turns and carries a steady current $I=2.0\,\text{A}$. The inner and outer radii are $a=4.0\,\text{cm}$ and $b=9.0\,\text{cm}$, respectively. Assume the magnetic field is negligible outside the windings and is approximately circular and tangent to a circle of radius $r$ inside the core region $a<r<b$. Consider an Amperian loop that is a circle of radius $r=5.0\,\text{cm}$ centered on the toroid axis. According to Ampère's Law, $\oint \vec B\cdot d\vec \ell=\mu_0 I_{\text{enc}},$ and by symmetry $\oint \vec B\cdot d\vec \ell=B(2\pi r)$ while $I_{\text{enc}}=NI$ because the loop links all turns. Use $\mu_0=4\pi\times10^{-7}\,\text{T}\cdot\text{m/A}$ and ignore fringing. According to Ampère's Law, determine the magnetic field within the toroid at a radius of $5.0\,\text{cm}$.
6. Two large, parallel, non-conducting plates are separated by a small distance. The plate on the left has a uniform positive surface charge density $+\sigma$, and the plate on the right has $-\sigma$. What are the magnitudes of the electric field between the plates ($E_{in}$) and to the right of the right plate ($E_{out}$)?
7. An ideal air-core solenoid has $N$ turns, a length ${\ell}$, and a cross-sectional area $A$. If the number of turns is tripled to $3N$ while the length and area remain constant, the new inductance will be...
8. At a specific point P in space, the net electric field is determined to be zero. Which of the following statements must be true?
9. What is the current through resistor 1 at time $t=0$, and what is the current through resistor 1 after a very long time ($t \to \infty$)?
10. Which of the following expressions correctly ranks the magnitudes of the currents?
11. A positive particle ($q=+2.0\times10^{-6}\,\text{C}$) moves at $v=1500\,(\text{m/s})$ north through a uniform magnetic field $B=0.80\,\text{T}$ directed east. Moving charges create magnetic fields, and the right-hand rule gives the direction of $\vec v\times\vec B$; the magnetic force magnitude is $F=qvB\sin\theta$. Refer to the scenario above. What is the direction of the magnetic force on a positive charge moving as described?
12. The dielectric constant κ of a material is defined as the ratio of which two quantities?
13. A series LR circuit with $V=15\,\text{V}$, $R=5\,\Omega$, $L=5\,\text{H}$ closes; Refer to the scenario above. How does the current change over time after the switch is closed?
14. A $12\,\text{V}$ ideal battery charges a $C=200\,\mu\text{F}$ capacitor through a resistor $R=300\,\Omega$; after a long time, the capacitor reaches $12\,\text{V}$. The capacitor then disconnects from the battery and discharges through the same resistor in a closed loop. During discharge, charge moves through a potential difference, so capacitor potential energy decreases and becomes thermal energy in $R$ (via brief carrier kinetic energy). The initial discharge energy is $U_0=\tfrac12 C V^2=\tfrac12(200\times10^{-6})(12^2)=1.44\times10^{-2}\,\text{J}$. With $RC=0.060\,\text{s}$, after $t=0.030\,\text{s}$, $U_C=U_0 e^{-2t/RC}=U_0 e^{-1}\approx5.30\times10^{-3}\,\text{J}$, so $9.1\times10^{-3}\,\text{J}$ has been converted to heat while total energy remains conserved. Based on the scenario, how does the energy stored in the capacitor change as it discharges?
15. Two identical light bulbs, each with resistance $R$, are connected to an ideal battery with voltage $V$. What is the ratio of the total power consumed when they are in parallel to the total power consumed when they are in series, $P_{\text{parallel}}/P_{\text{series}}$?
16. Two point charges are fixed in vacuum: $q_1=+3.0\times10^{-9}\ \text{C}$ and $q_2=-3.0\times10^{-9}\ \text{C}$. A point $P$ is $0.30\ \text{m}$ from each charge. Use superposition with $V=\sum \dfrac{kq_i}{r_i}$, where $k=8.99\times10^{9}$ (and $e=1.60\times10^{-19}\ \text{C}$). In the situation described, what is the electric potential at point $P$ due to the charge configuration?
17. In an ideal LC circuit, the charge on the capacitor $q(t)$ and the current in the inductor $I(t)$ oscillate sinusoidally. What is the phase difference between the charge oscillations and the current oscillations?
18. An electron is in a uniform electric field of magnitude $300 \text{ N/C}$ directed in the positive x-direction. What is the force on the electron?
19. An ideal solenoid of length ${\ell}$ and radius $r$ has $N$ turns of wire. Assuming the solenoid is long enough that end effects are negligible, its self-inductance is proportional to...
20. Electric charge (C) can be positive or negative; electric force is the interaction between charges and follows Coulomb's Law $F=k\dfrac{|q_1q_2|}{r^2}$. Two like point charges $q_1=+2.0\,\mu\text{C}$ and $q_2=+2.0\,\mu\text{C}$ are $0.30\,\text{m}$ apart on a line. A third point charge $q_3=+1.0\,\mu\text{C}$ is placed exactly midway between them. By superposition, the net force on $q_3$ equals the vector sum of the forces from $q_1$ and $q_2$. Explain the effect of introducing $q_3$ between the like charges by determining the net force on $q_3$.

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