AP Physics C: Electricity and Magnetism Unit 5 Practice Test & Exam | 18 Questions

Questions 1-3 refer to the following scenario.

1. Which of the following best describes the initial direction of the magnetic force on the proton as it enters the field?

(A)To the right(B)To the left(C)Upward, toward the top of the page(D)Downward, toward the bottom of the page

2. Which of the following expressions represents the magnitude of the radius of the proton's subsequent path?

(A)$\frac{mv}{eB}$(B)$\frac{eB}{mv}$(C)$\frac{mv^2}{eB}$(D)$\frac{eB}{mv^2}$

3. After the proton has been in the field for some time, its velocity vector makes an angle of 45° with its initial direction. What is the total work done on the proton by the magnetic field during this time?

(A)$0$(B)$eBv \cos(45^\circ)$(C)$\frac{1}{2}m(vf^2 - vi^2)$, where $vf > vi$(D)$-eBv \sin(45^\circ)$

Questions 4-6 refer to the following scenario.

4. What is the direction of the net magnetic field at point P?

(A)To the right(B)To the left(C)Upward, toward the top of the page(D)Downward, toward the bottom of the page

5. If $I1 = I2 = I$, what is the magnitude of the net magnetic field at point P?

(A)$0$(B)$\frac{\mu_0 I}{\pi d}$(C)$\frac{2\mu_0 I}{\pi d}$(D)$\frac{\mu_0 I}{2\pi d}$

6. What is the direction of the magnetic force exerted on Wire 1 by Wire 2?

(A)To the right, away from Wire 2(B)To the left, toward Wire 2(C)Upward, toward the top of the page(D)Downward, toward the bottom of the page

Questions 7-9 refer to the following scenario.

7. A student wants to use Ampère's Law, $\oint\vec{B}\cdot d\vec{l}=\mu{0}I{enc}$, to find the magnetic field inside the solenoid. Which of the following statements correctly justifies a step in the derivation?

(A)The contribution to the line integral from sides 2 and 4 is non-zero because the magnetic field is perpendicular to the path.(B)The contribution to the line integral from side 3 is non-zero because the current is enclosed by the loop.(C)The magnetic field is assumed to be zero outside the ideal solenoid, so the integral along side 3 is zero.(D)The enclosed current $I_{enc}$ is equal to the total current $I$ flowing in the wire.

8. What is the value of the line integral $\oint\vec{B}\cdot d\vec{l}$ for the Amperian loop shown?

(A)$0$(B)$BL$(C)$2BL + 2Bw$(D)$B(2L+2w)$

9. If the current in the solenoid is doubled and the number of turns per unit length is halved, how does the new magnetic field magnitude $B{new}$ inside the solenoid compare to the original magnitude $B{orig}$?

(A)$B{new} = \frac{1}{4} B{orig}$(B)$B{new} = \frac{1}{2} B{orig}$(C)$B{new} = B{orig}$(D)$B{new} = 2 B{orig}$

Refer to the figure below.

10. Which of the following diagrams best represents the magnetic field lines created by a bar magnet?

(A)Field lines originating from the north pole and terminating on the south pole.(B)Field lines forming closed loops that emerge from the north pole and enter the south pole.(C)Field lines pointing radially outward from the north pole and radially inward to the south pole.(D)Parallel, equally spaced field lines throughout the space around the magnet.

11. An electron is moving with a velocity $\vec{v} = (3 \times 10^5 \hat{i} - 4 \times 10^5 \hat{j})$ m/s in a uniform magnetic field $\vec{B} = (0.5 \hat{k})$ T. What is the magnetic force $\vec{F}_B$ on the electron? (The charge of an electron is $q = -1.6 \times 10^{-19}$ C).

(A)$(-3.2 \times 10^{-14} \hat{i} - 2.4 \times 10^{-14} \hat{j})$ N(B)$(3.2 \times 10^{-14} \hat{i} + 2.4 \times 10^{-14} \hat{j})$ N(C)$(-9.6 \times 10^{-14} \hat{k})$ N(D)$(0)$ N

12. A student is asked to find the magnetic field at a distance $r$ from the center of a very long, straight wire carrying a current $I$. The student considers using either the Biot-Savart law or Ampère's law. Which of the following provides the best justification for choosing Ampère's law?

(A)The Biot-Savart law only applies to finite wire segments, not infinitely long wires.(B)Ampère's law is a more fundamental law of magnetism than the Biot-Savart law.(C)The cylindrical symmetry of the current distribution means the magnetic field has a constant magnitude on a circular Amperian loop centered on the wire.(D)The magnetic field is uniform everywhere, which simplifies the line integral in Ampère's law.

13. A circular loop of wire with radius $R$ carries a current $I$. What is the magnitude of the magnetic field at the center of the loop?

(A)$B = \frac{\mu_0 I}{2R}$(B)$B = \frac{\mu_0 I}{2\pi R}$(C)$B = \mu_0 I R^2$(D)$B = 0$

14. Gauss's law for magnetism is given by the equation $\oint\vec{B}\cdot d\vec{A}=0$. The primary physical implication of this law is that:

(A)The net magnetic flux through any closed surface is zero.(B)Magnetic fields are created only by moving charges.(C)The magnetic force on a charged particle is always perpendicular to its velocity.(D)The magnetic field inside a conductor is always zero.

15. A segment of wire is bent into a semicircle of radius $R$ and carries a current $I$ as shown. The wire is in a uniform magnetic field $\vec{B}$ directed out of the page. What is the net magnetic force on the semicircular segment of wire?

(A)$0$(B)$\pi R I B$, directed downward(C)$2 R I B$, directed downward(D)$2 \pi R I B$, directed upward

16. A beam of ions, each with charge $q$ and mass $m$, enters a velocity selector, a region with a uniform electric field $\vec{E}$ pointing down and a uniform magnetic field $\vec{B}$ pointing into the page. The ions are initially traveling to the right. For which speed $v$ will the ions pass through the region undeflected?

(A)$v = \frac{E}{B}$(B)$v = \frac{B}{E}$(C)$v = q\frac{E}{B}$(D)$v = \frac{B^2}{E}$

17. A coaxial cable consists of a solid inner conductor of radius $a$ and a thin outer cylindrical shell of radius $b$. The inner conductor carries a current $I$ into the page, and the outer shell carries a current $I$ out of the page. What is the magnitude of the magnetic field at a distance $r$ from the center, such that $a < r < b$?

(A)$0$(B)$\frac{\mu_0 I}{2\pi r}$(C)$\frac{\mu_0 I}{2\pi} (\frac{1}{a} - \frac{1}{b})$(D)$\frac{\mu_0 I (b^2 - r^2)}{2\pi r (b^2 - a^2)}$

18. The Biot-Savart Law is given by $d\vec{B}=\frac{\mu_{0}}{4\pi}\frac{I(d\vec{l}\times\hat{r})}{r^{2}}$. Which of the following statements is a correct interpretation of this law? Section II: Free-Response FRQ 1[Skills: 2.A, 2.B, 3.A | Topic: 12.2] An electron of mass $m_e$ and charge $-e$ is accelerated from rest through a potential difference $\Delta V$. It then enters a region of uniform magnetic field of magnitude $B$, directed perpendicular to the electron's velocity. FRQ 2[Skills: 2.B, 3.B | Topic: 12.3] Consider a straight, finite wire of length $2L$ lying on the y-axis from $y = -L$ to $y = +L$. The wire carries a steady current $I$ in the $+y$ direction. You are asked to find the magnetic field at point P, located on the x-axis at a distance $x$ from the origin. FRQ 3[Skills: 1.A, 2.B, 2.C | Topic: 12.4] A long, hollow cylindrical conductor with inner radius $a$ and outer radius $b$ carries a total current $I$ distributed uniformly over its cross-section. The current flows into the page. FRQ 4[Skills: 3.A, 3.B | Topics: 12.1, 12.2, 12.3] Two long, straight, parallel wires, Wire A and Wire B, are separated by a distance $d$. Wire A carries current $IA$ and Wire B carries current $IB$.

(A)Explain how Wire A creates a magnetic field at the location of Wire B. Then, explain how this magnetic field exerts a force on Wire B.(B)Suppose the currents $IA$ and $IB$ are in the same direction. Determine if the force between the wires is attractive or repulsive. Justify your answer using an appropriate right-hand rule.(C)The force per unit length, $F/L$, that each wire exerts on the other is given by $\frac{F}{L} = \frac{\mu0 IA I_B}{2\pi d}$. This relationship is used to define the Ampere, the SI unit of current. If two parallel wires are 1 meter apart and the force per unit length is exactly $2 \times 10^{-7}$ N/m, what must be the current in each wire? Justify your numerical answer.(D)Now, let the wire become infinitely long ($L \to \infty$). Explain qualitatively why the result of the integral from part (c) should be identical to the result obtained using Ampère's Law for an infinitely long wire.

AP Physics C: Electricity and Magnetism Unit 5: Magnetic Fields and Electromagnetism Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics C: Electricity and Magnetism Unit 5: Magnetic Fields and Electromagnetism Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)