Practice Test 4 - 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 charged conductor of arbitrary shape is in electrostatic equilibrium. Which statement best describes the direction of the electric field vector at any point just outside the surface of the conductor?
2. Using Kirchhoff's Junction Rule, determine $I_2$ leaving junction D if $I_1=0.80\,\text{A}$ enters and $I_3=0.25\,\text{A}$ and $I_4=0.15\,\text{A}$ leave.
3. A materials experiment uses a uniformly charged solid sphere of radius $R=0.060\,\text{m}$ with total charge $Q=+1.2\,\mu\text{C}$; the electric field at an interior point $r=0.030\,\text{m}$ is needed to estimate polarization forces in $\text{N/C}$. The sphere is isolated in vacuum and centered at the origin. Assume charge density is uniform throughout the volume. Consider the setup described above. Using Gauss's Law, determine the electric field inside the charged sphere.
4. An electric field in a region is given by the expression $\vec{E} = (3x^2) \hat{i} \ \text{N/C}$, where $x$ is in meters. What is the electric flux through a square surface in the y-z plane with side length $L$ located at $x = 2.0$ m?
5. A student analyzes a series circuit with a battery and two different resistors, $R_1$ and $R_2$. The student claims, "The total power dissipated by the two resistors in series is the sum of the powers each would dissipate if connected individually to the same battery." Which of the following is a correct evaluation of this claim?
6. In a parallel-plate capacitor, the electric field between plates is approximately uniform and related to surface charge density by $E=\sigma/\varepsilon_0$. The plates have $\sigma=3.5\times10^{-7}\,\text{C/m}^2$ and separation $d=1.5\times10^{-3}\,\text{m}$. Use $\varepsilon_0=8.85\times10^{-12}\,\text{C}^2/(\text{N}\cdot\text{m}^2)$ and $\Delta V=Ed$ (magnitude). Based on the data, if the electric field is set by $\sigma$, what is the potential difference across the plates?
7. A circuit consists of an uncharged capacitor with capacitance $C$, a resistor with resistance $R$, and an ideal battery with emf $E$, all connected in series. A switch is closed at $t=0$. After a very long time ($t \to \infty$), what is the potential difference across the capacitor?
8. A battery with emf $\varepsilon=18\,\text{V}$ and internal resistance $r=2.0\,\Omega$ is connected in series with an external resistor $R=7.0\,\Omega$ to form one closed loop. Using the loop rule, what is the potential difference across the battery terminals while the circuit is operating?
9. The behavior of the charge $q$ in an ideal LC circuit is described by the differential equation $\frac{d^2q}{dt^2} + 2500q = 0$, where $q$ is in coulombs and $t$ is in seconds. What is the angular frequency of the oscillation?
10. A fully charged capacitor is discharged through a resistor. The time constant $τ$ of the circuit represents the time required for the charge on the capacitor to decrease to approximately what percentage of its initial value?
11. At what rate is energy being stored in the magnetic field of the inductor at time $t=0$?
12. A coaxial cylindrical capacitor has a length $L$, an inner conductor of radius $a$, and an outer conductor of radius $b$. Its capacitance is given by $C = \frac{2\pi\epsilon_0 L}{\ln(b/a)}$. If the inner radius $a$ is halved and the outer radius $b$ is doubled, how does the new capacitance $C'$ compare to the original capacitance $C$?
13. The electric field in a region is given by $\vec{E} = c y^2 \hat{j}$, where $c$ is a constant. Which of the following integrals represents the electric flux through a rectangular area of width $w$ (in the x-direction) and length $l$ (in the z-direction) located in the xz-plane?
14. An infinite current sheet with surface current density $K$ produces a magnetic field of magnitude $\frac{\mu_0 K}{2}$ on either side. Which Amperian loop geometry is most appropriate for this derivation?
15. An imaginary closed spherical surface completely encloses the north pole of a bar magnet while the south pole is outside the surface. What is the net magnetic flux through the spherical surface?
16. A closed cubical surface of side length $L$ is placed in a uniform electric field that is directed along the x-axis. What is the net electric flux through the entire surface of the cube?
17. A proton ($q=+e$) moves from point A to point B in an electrostatic field inside an insulated chamber, so no external work is done and no energy leaves the system. The potential difference is $\Delta V = V_B - V_A = -500\,\text{V}$. The change in electric potential energy is $\Delta U = q\Delta V = (1.60\times10^{-19})(-500)=-8.0\times10^{-17}\,\text{J}$. If the proton starts with kinetic energy $K_i=2.0\times10^{-17}\,\text{J}$, then energy conservation gives $K_f = K_i - \Delta U = 1.0\times10^{-16}\,\text{J}$. The potential energy decrease equals the kinetic energy increase, showing interplay between $U$ and $K$ driven by potential difference. In the context of this scenario, what is the relationship between potential difference and energy conservation in the context?
18. A flat rectangular sheet is initially oriented such that its surface normal is parallel to a uniform electric field, resulting in a flux $\Phi_0$. The sheet is then rotated by 90 degrees about an axis that lies within the plane of the sheet. What is the new electric flux through the sheet?
19. Which of the following statements correctly describes the system in its final state?
20. The electric potential energy of a system consisting of a point charge $q$ and a fixed point charge $Q$ is $U(r) = kQq/r$. Which of the following describes the work done by the electric field as the charge $q$ is moved from an initial distance $R$ to a final distance $3R$?

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