AP Physics 2: Algebra-Based Unit 4: Magnetism and Electromagnetism Practice Exam

Assessment for Unit 4: Magnetism and Electromagnetism

Estimated Time: 60 minutes

Exam Details

Questions: 27 total (27 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 4: Magnetism and Electromagnetism
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (27 Questions)

Select the one best answer for each question.

1. [Skill: 1.1 | Topic: 4.1] A student is tasked with drawing the magnetic field lines surrounding a standard bar magnet. Which of the following best describes the required characteristics of the field lines to accurately represent the magnetic field $\vec{B}$?

(A)The lines must originate at the north pole and terminate at the south pole, forming open-ended paths that represent the strength of the pole.(B)The lines must form closed loops, exiting the north pole and entering the south pole outside the magnet, while continuing from the south pole to the north pole inside the magnet.(C)The lines must be drawn perpendicular to each other to show that the magnetic field is a vector quantity with independent components.(D)The lines must originate at both the north and south poles and extend infinitely outward to show the range of the magnetic force.

2. [Skill: 7.1 | Topic: 4.1] A permanent bar magnet is snapped into two equal pieces exactly halfway between the North and South poles. Which of the following correctly predicts the magnetic properties of the two resulting pieces?

(A)One piece will consist only of a North pole, and the other piece will consist only of a South pole.(B)Both pieces will lose their magnetic properties because the alignment of the microscopic dipoles is disrupted by the physical break.(C)Two smaller, complete magnets are created, each having its own North and South pole.(D)The magnetic field of each piece will be exactly half the strength of the original, but the pieces will only have one pole each.

3. [Skill: 5.1 | Topic: 4.1] A scientist is calculating the magnetic field inside a vacuum-sealed chamber and uses the constant $\mu_0$ in their equations. If the chamber is then filled with a material that has a high magnetic permeability, how will the physical relationship expressed by the equations change?

(A)The value of $\mu_0$ will increase because the vacuum permeability depends on the surrounding medium.(B)The magnetic field strength will likely increase because the material's permeability $\mu$ is greater than the vacuum permeability $\mu_0$.(C)The magnetic field strength will decrease because the material acts as an insulator against magnetic flux.(D)The equations will remain identical because $\mu_0$ is a universal constant that applies to all matter and space equally.

4. [Skill: 2.2 | Topic: 4.2] A particle with a charge of $+2.0 \times 10^{-6}$ C enters a uniform magnetic field of magnitude $0.50$ T with a speed of $1.0 \times 10^{4}$ m/s. The velocity vector of the particle makes an angle of $30^\circ$ with the magnetic field lines. What is the magnitude of the magnetic force exerted on the particle?

(A)0.005 Newtons(B)0.010 Newtons(C)0.0087 Newtons(D)Zero Newtons

5. [Skill: 6.4 | Topic: 4.2] A charged particle moves through a uniform magnetic field $\vec{B}$. Which of the following changes would result in the magnetic force on the particle doubling in magnitude? I. Doubling the speed of the particle. II. Doubling the magnitude of the magnetic field. III. Changing the angle between velocity and the field from $90^\circ$ to $180^\circ$.

(A)I only(B)II only(C)I or II only(D)I, II, or III

6. [Skill: 2.2 | Topic: 4.3] A straight segment of wire with a length of $0.50\text{ m}$ carries a current of $4.0\text{ A}$ in the $+x$ direction. The wire is immersed in a uniform magnetic field of magnitude $0.30\text{ T}$ that is directed in the $+y$ direction. What is the magnitude and direction of the magnetic force exerted on the wire segment?

(A)0.60 N in the +z direction (out of the page)(B)0.60 N in the -z direction (into the page)(C)1.2 N in the +z direction (out of the page)(D)0.0 N, because the current and field are not parallel

7. [Skill: 5.1 | Topic: 4.3] A student conducts an experiment to determine the relationship between the magnetic field $B$ and the distance $r$ from a long, straight wire carrying a constant current $I$. The student collects data for $B$ at various distances and intends to create a linear graph to verify the theoretical model $B = \frac{\mu_0 I}{2\pi r}$. Which of the following quantities should be plotted on the horizontal axis to yield a linear graph, and what would the slope of that graph represent?

(A)Plot $r$ on the horizontal axis; the slope represents $\frac{\mu_0 I}{2\pi}$.(B)Plot $r^2$ on the horizontal axis; the slope represents $\frac{\mu_0 I}{2\pi}$.(C)Plot $1/r$ on the horizontal axis; the slope represents $\frac{\mu_0 I}{2\pi}$.(D)Plot $1/r^2$ on the horizontal axis; the slope represents $\frac{\mu_0 I}{2\pi}$.

8. [Skill: 1.4 | Topic: 4.4] A square conducting loop with side length $s$ is placed in a uniform magnetic field of magnitude $B$. Initially, the plane of the loop is perpendicular to the magnetic field lines. The loop is then rotated $90^{\circ}$ about an axis through its center until the plane of the loop is parallel to the magnetic field lines. Which of the following expressions correctly represents the magnitude of the change in magnetic flux $\Delta \Phi_B$ through the loop during this rotation?

(A)0(B)$Bs$(C)$Bs^2$(D)$2Bs^2$

9. [Skill: 2.2 | Topic: 4.4] A stationary circular loop of wire with an area of $0.50\text{ m}^2$ is placed in a uniform magnetic field that is directed perpendicular to the plane of the loop. The magnetic field strength changes from $2.0\text{ T}$ to $6.0\text{ T}$ over a time interval of $4.0\text{ s}$. What is the magnitude of the average induced electromotive force (emf) in the loop during this time?

(A)0.50 V(B)0.80 V(C)2.0 V(D)8.0 V

10. [Skill: 1.1 | Topic: 4.1] A student places a small compass at various locations around a permanent bar magnet. Which of the following best describes the characteristics of the magnetic field $\vec{B}$ represented by the compass needle alignment? (A) The magnetic field lines originate at the North pole and terminate at the South pole, forming open-ended vectors. (B) The magnetic field is a vector quantity that points in the direction that the North pole of the compass needle points. (C) The strength of the magnetic field is uniform at all points surrounding the bar magnet. (D) The magnetic field lines only exist outside of the magnet, as the interior of a solid magnet cannot contain a field.

(A)The magnetic field lines originate at the North pole and terminate at the South pole, forming open-ended vectors.(B)The magnetic field is a vector quantity that points in the direction that the North pole of the compass needle points.(C)The strength of the magnetic field is uniform at all points surrounding the bar magnet.(D)The magnetic field lines only exist outside of the magnet, as the interior of a solid magnet cannot contain a field.

Refer to the figure below.

11. [Skill: 1.4 | Topic: 4.1] An iron rod is initially unmagnetized. It is then placed inside a strong, constant external magnetic field $\vec{B}_{ext}$ for a long period of time. Which of the following correctly explains the resulting change in the rod's microscopic structure and its macroscopic behavior? (A) The external field creates new magnetic monopoles within the iron, turning one end into a pure North pole. (B) The external field causes the randomly oriented atomic magnetic dipoles to align with $\vec{B}_{ext}$, creating a net magnetic field. (C) The protons within the iron atoms begin to flow in a circular path, creating a macroscopic current that generates a field. (D) The magnetic permeability of the iron rod decreases until it reaches the value of vacuum permeability $\mu_0$.

(A)The external field creates new magnetic monopoles within the iron, turning one end into a pure North pole.(B)The external field causes the randomly oriented atomic magnetic dipoles to align with $\vec{B}_{ext}$, creating a net magnetic field.(C)The protons within the iron atoms begin to flow in a circular path, creating a macroscopic current that generates a field.(D)The magnetic permeability of the iron rod decreases until it reaches the value of vacuum permeability $\mu_0$.

12. [Skill: 1.1 | Topic: 4.1] A scientist is performing an experiment in a vacuum chamber. She calculates the magnetic field strength near a current-carrying wire using the constant $\mu_0$. If she repeats the experiment in a medium with a magnetic permeability $\mu$ that is significantly higher than $\mu_0$, how will the magnetic field strength $B$ at the same distance from the wire change, and why? (A) $B$ will increase because the material's permeability enhances the field produced by the current. (B) $B$ will decrease because a higher permeability material absorbs the magnetic field lines. (C) $B$ will remain the same because $\mu_0$ is a fundamental constant of the universe that cannot be exceeded. (D) $B$ will remain the same because magnetic field strength only depends on the magnitude of the current $I$.

(A)$B$ will increase because the material's permeability enhances the field produced by the current.(B)$B$ will decrease because a higher permeability material absorbs the magnetic field lines.(C)$B$ will remain the same because $\mu_0$ is a fundamental constant of the universe that cannot be exceeded.(D)$B$ will remain the same because magnetic field strength only depends on the magnitude of the current $I$.

13. [Skill: 1.1 | Topic: 4.1] A long bar magnet is broken into two equal pieces. A student claims that one piece will now be a 'North-only' magnet and the other will be a 'South-only' magnet. Which of the following evidence-based statements best refutes the student's claim? (A) Magnetic field lines must form closed loops, requiring every magnet to have both a North and a South pole to allow the lines to return. (B) The magnetic permeability of the material changes when the magnet is broken, neutralizing the individual poles. (C) Breaking the magnet destroys the alignment of the microscopic dipoles, resulting in two unmagnetized pieces of iron. (D) Gauss's Law for Magnetism states that the total magnetic flux through a closed surface is proportional to the enclosed magnetic charge.

(A)Magnetic field lines must form closed loops, requiring every magnet to have both a North and a South pole to allow the lines to return.(B)The magnetic permeability of the material changes when the magnet is broken, neutralizing the individual poles.(C)Breaking the magnet destroys the alignment of the microscopic dipoles, resulting in two unmagnetized pieces of iron.(D)Gauss's Law for Magnetism states that the total magnetic flux through a closed surface is proportional to the enclosed magnetic charge.

14. [Skill: 1.4 | Topic: 4.2] A proton is moving with a constant velocity $\vec{v}$ in the $+x$ direction. It enters a region of space containing a uniform magnetic field $\vec{B}$ directed in the $+y$ direction. In which direction is the magnetic force $\vec{F}_B$ exerted on the proton at the instant it enters the field?

(A)In the $+z$ direction (out of the page)(B)In the $-z$ direction (into the page)(C)In the $+y$ direction(D)The force is zero

15. [Skill: 2.2 | Topic: 4.2] Particle 1 has a charge $q$ and moves with speed $v$ perpendicular to a uniform magnetic field of magnitude $B$, experiencing a magnetic force of magnitude $F$. Particle 2 has a charge $2q$ and moves with speed $2v$ at an angle of $30^{\circ}$ relative to the same magnetic field. What is the magnitude of the magnetic force exerted on Particle 2 in terms of $F$?

(A)$F$(B)$2F$(C)$4F$(D)$0.5F$

16. [Skill: 1.4 | Topic: 4.2] A small sphere with a net positive charge is moving at a constant velocity in the $+z$ direction (out of the page). At a specific moment, the sphere passes the origin. What is the direction of the magnetic field produced by this moving charge at a point located on the $+x$ axis?

(A)In the $+x$ direction(B)In the $+y$ direction(C)In the $-y$ direction(D)In the $+z$ direction

17. [Skill: 1.4 | Topic: 4.2] An alpha particle (charge $+2e$) and an electron (charge $-e$) both enter a uniform magnetic field with the same velocity $\vec{v}$. The velocity is perpendicular to the magnetic field. Which of the following correctly compares the magnitudes of the magnetic forces $F_{\alpha}$ and $F_e$ and the directions of the forces exerted on the particles?

(A)$F_{\alpha} = 2F_e$, and the forces are in the same direction.(B)$F_{\alpha} = 2F_e$, and the forces are in opposite directions.(C)$F_{\alpha} = 0.5F_e$, and the forces are in opposite directions.(D)$F_{\alpha} = F_e$, and the forces are in the same direction.

18. [Skill: 2.B | Topic: 4.3] A student conducts an experiment to measure the magnetic field magnitude $B$ at various perpendicular distances $r$ from a long, straight wire carrying a constant current $I$. Which of the following procedures would allow the student to create a linear graph to confirm the relationship between $B$ and $r$?

(A)Graph $B$ on the vertical axis and $r$ on the horizontal axis.(B)Graph $B$ on the vertical axis and $r^2$ on the horizontal axis.(C)Graph $B$ on the vertical axis and $\frac{1}{r}$ on the horizontal axis.(D)Graph $B$ on the vertical axis and $\frac{1}{r^2}$ on the horizontal axis.

19. [Skill: 1.B | Topic: 4.3] A long straight wire is oriented vertically and carries a conventional current $I$ directed upward toward the top of the page. A small compass is placed at a point $P$ located directly to the right (East) of the wire. In which direction will the North pole of the compass needle point due to the magnetic field of the wire?

(A)Toward the top of the page (North)(B)Toward the bottom of the page (South)(C)Into the page(D)Out of the page

20. [Skill: 5.B | Topic: 4.3] A straight segment of wire with length $L = 0.50$ m carries a current $I = 2.0$ A. The wire is placed in a uniform magnetic field of magnitude $B = 0.40$ T. If the magnetic force exerted on the wire segment is measured to be $0.20$ N, what is the angle $\theta$ between the direction of the current and the direction of the magnetic field?

(A)$0^\circ$(B)$30^\circ$(C)$45^\circ$(D)$90^\circ$

Refer to the figure below.

21. [Skill: 1.C | Topic: 4.3] Two long, parallel wires are separated by a distance $d$. Wire 1 carries a current $I$ directed toward the top of the page. Wire 2 carries a current $2I$ directed toward the bottom of the page. Which of the following correctly describes the magnetic force exerted on Wire 2 by Wire 1?

(A)A force directed to the left, toward Wire 1.(B)A force directed to the right, away from Wire 1.(C)A force directed into the page.(D)Zero, because the currents are in opposite directions.

22. [Skill: 2.B | Topic: 4.4] Questions 1 and 2 refer to the following stimulus: A circular conducting loop of radius $r$ is placed in a uniform magnetic field of magnitude $B$. The field is oriented at an angle $\theta = 60^{\circ}$ relative to the normal to the plane of the loop. What is the magnetic flux $\Phi_B$ through the loop?

(A)$\Phi_B = 0$(B)$\Phi_B = \frac{1}{2} B \pi r^2$(C)$\Phi_B = \frac{\sqrt{3}}{2} B \pi r^2$(D)$\Phi_B = B \pi r^2$

23. [Skill: 5.D | Topic: 4.4] Refer to the stimulus from Question 1. The magnetic field magnitude $B$ begins to decrease at a constant rate such that $B(t) = B_0 - kt$, where $k$ is a positive constant. Which of the following expressions correctly represents the magnitude of the induced electromotive force (emf) $|mathcal{E}|$ in the loop during this time?

(A)$|\mathcal{E}| = k \pi r^2$(B)$|\mathcal{E}| = (B_0 - kt) \pi r^2 \cos 60^{\circ}$(C)$|\mathcal{E}| = \frac{1}{2} k \pi r^2$(D)$|\mathcal{E}| = k \cos 60^{\circ}$

Refer to the figure below.

24. [Skill: 1.C | Topic: 4.4] Questions 3 and 4 refer to the following stimulus: [Image Cue]: Diagram showing a stationary circular wire loop in the plane of the page. A bar magnet is positioned above the center of the loop with its North pole (N) pointing downward toward the loop. The magnet is then moved rapidly downward toward the loop. As the magnet moves toward the loop, what is the direction of the induced current in the loop as viewed from above, and what is the direction of the magnetic force exerted by the loop on the magnet?

(A)Current: Clockwise; Force: Upward(B)Current: Clockwise; Force: Downward(C)Current: Counterclockwise; Force: Upward(D)Current: Counterclockwise; Force: Downward

25. [Skill: 2.C | Topic: 4.4] Refer to the stimulus from Question 3. A second experiment is performed where the original loop is replaced by a loop made of the same material and wire thickness, but with double the radius ($2r$). The magnet is moved toward the loop with the same constant velocity. How does the maximum induced emf $\mathcal{E}_{new}$ and the maximum induced current $I_{new}$ in the larger loop compare to the original loop values ($\mathcal{E}_{old}$ and $I_{old}$)?

(A)$\mathcal{E}_{new} = 2\mathcal{E}_{old}$ and $I_{new} = I_{old}$(B)$\mathcal{E}_{new} = 4\mathcal{E}_{old}$ and $I_{new} = 2I_{old}$(C)$\mathcal{E}_{new} = 4\mathcal{E}_{old}$ and $I_{new} = 4I_{old}$(D)$\mathcal{E}_{new} = 2\mathcal{E}_{old}$ and $I_{new} = 2I_{old}$

Refer to the figure below.

26. [Skill: 2.B | Topic: 4.4] A square loop of wire with side length $s$ and total resistance $R$ moves with a constant speed $v$ to the right. The loop enters a region of uniform magnetic field $B$ that is directed into the page and has a sharp vertical boundary at $x = 0$. Which of the following best describes the magnitude of the induced emf $|\mathcal{E}|$ in the loop as a function of the position $x$ of the right-hand side of the loop as it passes from $x = 0$ to $x = 2s$? [Image Cue]: Diagram of a square wire loop with side $s$ moving with velocity $v$ toward a shaded region. The shaded region represents a uniform magnetic field $B$ directed into the page (indicated by 'x' symbols). The left vertical boundary of the shaded region is labeled $x = 0$.

(A)$|\mathcal{E}|$ is constant at $Bsv$ for $0 < x < s$ and is zero for $s < x < 2s$.(B)$|\mathcal{E}|$ increases linearly from $0$ to $Bsv$ for $0 < x < s$ and remains at $Bsv$ for $s < x < 2s$.(C)$|\mathcal{E}|$ is zero for $0 < x < s$ and is constant at $Bsv$ for $s < x < 2s$.(D)$|\mathcal{E}|$ is constant at $Bsv$ for the entire interval $0 < x < 2s$.

Refer to the figure below.

27. [Skill: 1.4 | Topic: 4.2] An electron (charge $-e$) and a proton (charge $+e$) are both moving with the same constant speed $v$ in the $+x$-direction. They enter a region containing a uniform magnetic field $\vec{B}$ directed into the page (the $-z$-direction). Which of the following correctly compares the magnitudes and directions of the initial magnetic forces exerted on the electron and the proton? [Image Cue]: A diagram showing an electron and a proton moving to the right (labeled $+x$) toward a rectangular region filled with 'x' symbols representing a magnetic field directed into the page. A coordinate axis is provided showing $+x$ to the right and $+y$ toward the top of the page.

(A)The magnitudes of the forces are equal; the electron is initially deflected toward the top of the page ($+y$), and the proton is initially deflected toward the bottom of the page ($-y$).(B)The magnitudes of the forces are equal; the electron is initially deflected toward the bottom of the page ($-y$), and the proton is initially deflected toward the top of the page ($+y$).(C)The magnitude of the force on the proton is greater than the force on the electron; both particles are initially deflected toward the top of the page ($+y$).(D)The magnitude of the force on the electron is greater than the force on the proton; both particles are initially deflected toward the bottom of the page ($-y$).

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