AP Physics C: E&M Unit 12 practice questions
Try 10 multiple-choice questions from Unit 12 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.
Question 1
Two long, straight, parallel wires carry currents I₁ and I₂ in opposite directions. A student claims that the wires repel each other. Which of the following correctly justifies this claim using the Biot-Savart law and the magnetic force law?
The magnetic field from one wire is perpendicular to the other, creating a repulsive force directed away from the source.
The magnetic field from one wire is parallel to the other, creating a repulsive force directed away from the source.
The magnetic field from one wire is perpendicular to the other, creating an attractive force directed toward the source.
The magnetic field from one wire is parallel to the other, creating an attractive force directed toward the source.
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Answer: (A)
Applying the right-hand rule for the Biot-Savart law shows that the magnetic field from the first wire is directed into the page at the location of the second wire. Since the currents are antiparallel, the cross product of the current vector and the magnetic field vector results in a force directed radially outward, causing repulsion.
Question 2
A long straight wire carries current to the right. A rectangular loop is placed above the wire with its closest side parallel to the wire. The loop carries a clockwise current. A student claims the loop experiences a net repulsive force. Which statement best supports this claim?
The repulsive force on the closer segment exceeds the attractive force on the farther segment due to the magnetic field gradient.
The attractive force on the closer segment exceeds the repulsive force on the farther segment due to the magnetic field gradient.
The repulsive force on the closer segment equals the attractive force on the farther segment due to the loop's symmetry.
The attractive force on the closer segment equals the repulsive force on the farther segment due to the loop's symmetry.
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Answer: (A)
The bottom segment of the loop carries current to the left (antiparallel to the wire), creating a repulsive force, while the top segment carries current to the right (parallel), creating an attractive force. Since the magnetic field strength decreases with distance (1/r), the repulsive force on the closer bottom segment is stronger than the attractive force on the farther top segment.
Question 3
A rigid wire segment of length L lies along the x-axis carrying current I in the +x direction. The wire is immersed in a magnetic field B = βx k̂. A student calculates the net magnetic force to be F = -0.5βIL² ĵ. Which of the following correctly justifies this result?
Integrating the cross product of the current element and the variable magnetic field vector yields a net force in the negative y-direction.
Integrating the cross product of the current element and the constant magnetic field magnitude yields a net force in the negative y-direction.
Integrating the cross product of the current element and the variable magnetic field vector yields a net force in the positive y-direction due to the direction of current flow.
Integrating the magnitude of the current element times the variable magnetic field magnitude yields a net force in the negative y-direction.
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Answer: (A)
The differential force is dF = I(dx î) × (βx k̂). Since î × k̂ = -ĵ, the direction is correct. Integrating βx from 0 to L yields a factor of L²/2, confirming the magnitude and direction of the calculated force.
Question 4
A flexible circular conducting loop carries a current I in a uniform magnetic field B directed perpendicular to the plane of the loop. A student observes the loop stretching outward to maximize its area. Which statement correctly justifies this behavior?
The cross product of the tangential current vector and the perpendicular magnetic field creates a force directed radially outward.
The cross product of the tangential current vector and the perpendicular magnetic field creates a force directed radially inward.
The dot product of the tangential current vector and the perpendicular magnetic field creates a force directed radially outward.
The cross product of the radial current vector and the perpendicular magnetic field creates a force directed tangentially outward.
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Answer: (A)
At every point on the circle, the current vector is tangential and the magnetic field is perpendicular. The cross product of these vectors results in a magnetic force directed radially outward from the center, causing the flexible loop to expand.
Question 5
A student proposes a theoretical magnetic charge distribution where magnetic field lines radiate outward from a single point source to infinity. Which fundamental principle of electromagnetism refutes the existence of this field configuration?
Gauss's law for magnetism, which requires net magnetic flux through any closed surface to be zero
Gauss's law for electricity, which requires net electric flux to be proportional to enclosed charge
Ampère's law, which relates the magnetic field circulation to the enclosed electric current
Faraday's law, which relates the induced electromotive force to the rate of change of magnetic flux
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Answer: (A)
Applying Gauss's law for magnetism () reveals that magnetic field lines must form closed loops and cannot diverge from a single point source (monopole).
Question 6
A permanent bar magnet with a North pole at one end and a South pole at the other is cut in half perpendicular to its long axis. A student claims that one piece will be a pure North pole and the other a pure South pole. Which statement correctly evaluates this claim using magnetic domain theory?
Incorrect; atomic dipoles align to create new North and South poles on the cut faces of each piece
Incorrect; atomic dipoles at the cut surface remain unaligned, preventing new poles from forming on either piece
Correct; atomic dipoles separate into isolated North and South poles that cannot recombine into new dipoles
Incorrect; atomic dipoles redistribute uniformly throughout each piece rather than concentrating at the cut faces
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Answer: (A)
Applying the model of atomic magnetic dipoles shows that cutting a magnet merely separates chains of aligned dipoles, leaving a North pole on one cut face and a South pole on the other.
Question 7
A student sketches magnetic field lines for a bar magnet, showing them originating at the North pole, traveling outside, and terminating at the South pole, with no lines inside the magnet. Which property of magnetic fields does this sketch violate?
Magnetic field lines form continuous closed loops, so they must continue from South to North inside
Magnetic field lines form continuous closed loops, so they must continue from North to South inside
Magnetic field lines originate on positive poles and terminate on negative poles like electric fields
Magnetic field lines originate on negative poles and terminate on positive poles like electric fields
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Answer: (A)
Applying Gauss's law for magnetism requires field lines to be continuous loops; they cannot start or stop, so they must pass through the magnet's interior.
Question 8
A closed cylindrical surface encloses a bar magnet and a current-carrying loop of wire. A student calculates the net magnetic flux through the cylinder's surface to be non-zero. Which application of Maxwell's equations correctly assesses this result?
The result is incorrect because Gauss's law for magnetism mandates zero net flux through any closed surface
The result is incorrect because Ampère's law mandates zero net circulation around any closed current loop
The result is correct because the enclosed current loop generates a net magnetic flux through the surface
The result is correct because the enclosed bar magnet generates a net magnetic flux through the surface
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Answer: (A)
Applying Maxwell's second equation () confirms that the net magnetic flux through any closed surface must be zero, regardless of enclosed sources.
Question 9
A researcher measures the magnetic field magnitude along the axis of a small magnetic dipole. If the distance from the dipole center doubles from to , how does the field magnitude change, assuming is large compared to the dipole size?
It decreases by a factor of 8, because the field of a dipole is proportional to
It decreases by a factor of 4, because the field of a dipole is proportional to
It decreases by a factor of 2, because the field of a dipole is proportional to
It remains constant, because the field of a dipole is uniform along the dipole axis
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Answer: (A)
Applying the theoretical relationship for a magnetic dipole field () shows that doubling the distance reduces the field by .
Question 10
A uniform magnetic field passes through a hemispherical surface of radius and a circular disk of radius that shares the same boundary. A student claims the magnitude of magnetic flux is the same for both surfaces. Which principle supports this?
Gauss's law for magnetism implies flux depends only on the boundary of the open surface
Gauss's law for electricity implies flux depends only on the charge enclosed by the surface
Ampère's law implies flux depends only on the current passing through the surface boundary
Faraday's law implies flux depends only on the time rate of change of the magnetic field
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Answer: (A)
Since the net flux through the closed surface (hemisphere + disk) is zero (), the flux through the hemisphere must equal the flux through the disk.
What's on the AP Physics C: E&M Unit 12 practice test
The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:
- 20 Multiple Choice Questions (40 minutes)
- 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
- 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)
Questions are drawn from 1099 multiple-choice questions and 41 FRQs written for Unit 12, Magnetic Fields & Electromagnetism.
Practice AP Physics C: E&M Unit 12 FRQs
Answer the unit's free-response questions one at a time and get a score on every part.
- FRQ 1 – Mathematical Routines (10 questions)
- FRQ 2 – Translation Between Representations (1 question)
- FRQ 3 – Experimental Design (15 questions)
- FRQ 4 – Qualitative/Quantitative Translation (15 questions)
Review Unit 12 before you start
- 12.1 Magnetic Fields
- 12.2 Magnetism and Moving Charges
- 12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
- 12.4 Ampère's Law