Practice Test 3 - AP Physics C Electricity and Magnetism

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

Start practice test

1. A uniform electric field has magnitude $E=8.00\times10^{2}\ \text{V/m}$ and points in the $-x$ direction. Points $A$ and $B$ are separated by $d=0.060\ \text{m}$ along $+x$. Use $\Delta V=-\vec E\cdot\Delta\vec r$ (and $k=8.99\times10^{9}$, $e=1.60\times10^{-19}\ \text{C}$). In the situation described, calculate the potential difference $V_B-V_A$.
2. A proton is released from rest in a uniform electric field of magnitude $1.0 \times 10^5 \text{ N/C}$. What is the magnitude of its initial acceleration?
3. A $10 \, \mu\text{F}$ capacitor is charged to a potential difference of $20 \text{ V}$. It is then disconnected from the charging source and connected at $t=0$ to a network of resistors. The network consists of a $2 \, \Omega$ resistor in series with a parallel combination of a $3 \, \Omega$ resistor and a $6 \, \Omega$ resistor. What is the initial current flowing from the capacitor?
4. A square loop of wire is pulled at a constant speed $v$ first into a uniform magnetic field region, and then later pulled out of the same region at the same constant speed $v$. Let $F_{in}$ be the magnitude of the magnetic force on the loop as it enters, and $F_{out}$ be the magnitude as it exits. How do $F_{in}$ and $F_{out}$ compare?
5. A conducting sphere of radius $R$ has an initial charge of $-6 \mu C$. It is connected by a very long wire to a distant conducting sphere of radius $2R$ that has an initial charge of $+15 \mu C$. After electrostatic equilibrium is reached, what is the final charge on the smaller sphere?
6. An electron with initial velocity $v_0$ enters a region of uniform electric field $E$ directed perpendicular to its velocity. The region is between the plates of a large parallel-plate capacitor. Neglecting any edge effects and gravitational forces, which of the following best describes the path of the electron while it is in the electric field?
7. A thin spherical shell has radius $0.40\ \text{m}$ and total charge $+5.0\ \mu\text{C}$. Based on the scenario described, what is the electric field magnitude at $r=0.20\ \text{m}$ ($\varepsilon_0=8.85\times10^{-12}$)?
8. A charged object $X$ is used to charge a conductor $Y$ by induction. Which of the following statements is true about the charge on $Y$?
9. A hollow, uncharged, conducting spherical shell is placed in a region of space with no external electric fields. What is the magnitude of the electric field inside the empty cavity of the shell?
10. A long air-core solenoid has turn density $n=1200\,\text{m}^{-1}$ and carries a steady current $I=0.80\,\text{A}$. The solenoid length is much greater than its radius, so the magnetic field inside is approximately uniform and axial, and the magnetic field outside is approximately zero. Choose a rectangular Amperian loop with length $\ell$ inside the solenoid parallel to the axis and the return path outside. According to Ampère's Law, $\oint \vec B\cdot d\vec \ell=\mu_0 I_{\text{enc}},$ with $\mu_0=4\pi\times10^{-7}\,\text{T}\cdot\text{m/A}$. Using the symmetry assumptions, the integral reduces to $B\ell$ for the inside segment, and $I_{\text{enc}}=(n\ell)I$ because $n\ell$ turns are enclosed. Ignore fringing and assume the current is steady. According to Ampère's Law, calculate the magnetic field inside the solenoid.
11. A battery drives a steady current $I=2.0\,\text{A}$ through a single-loop circuit with one resistor. Charge is not created or destroyed; it redistributes in the conducting wires while the surrounding plastic insulation prevents charge leakage. Based on the described process, how does the current in the wire change as it passes through the resistor?
12. A cylindrical wire of ohmic material has its length doubled, while its total volume is kept constant. By what factor does its resistance change?
13. A space heater is modeled as a single resistor of $R=24\,\Omega$ connected across a $120\,\text{V}$ outlet. The heater is the only load, so the voltage across the resistor equals the source voltage. Use $P=\frac{V^2}{R}$ to compute the electrical power converted to heat. Report the power in watts (W). Determine the power consumed by the appliance.
14. What is the final state of the conducting sphere?
15. A small magnetic compass is placed at a point in space. The direction that the north-seeking pole of the compass needle points indicates which of the following?
16. A positive ion ($q=+1.60\times10^{-19}\,\text{C}$) enters a uniform magnetic field $\vec B=0.50\,\text{T}$ directed into the page. Its velocity is $v=2.0\times10^{6}\,\text{m/s}$ to the right, so moving charge produces no $\vec B$ here but feels Lorentz force $\vec F=q\,\vec v\times\vec B$. Use the right-hand rule for $\vec v\times\vec B$. Refer to the scenario above. What is the direction of the magnetic force on a positive charge moving as described?
17. What is the ratio of the parallel current to the series current, $I_P / I_S$?
18. An isolated parallel-plate capacitor has plates of area $A$ separated by a distance $d$. It holds a net charge of magnitude $Q$ on each plate. What is the magnitude of the electrostatic force exerted by one plate on the other?
19. A cylindrical wire has length $L$, radius $r$, and is made of a material with resistivity $\rho$. If a potential difference $V$ is applied between the ends of the wire, what is the power dissipated in the wire?
20. A square conducting loop of mass $m$, side length $L$, and resistance $R$ is released from rest. At the instant its top edge enters a uniform magnetic field $B$ directed into the page, the loop has a downward speed $v$. What is the magnitude of the net force on the loop at this instant?

Practice tests