Magnetism and Current-Carrying Wires - AP Physics 2

1. Two long parallel wires $2.0\,\text{cm}$ apart carry equal currents: left wire upward, right wire downward. Which statement best describes the interaction between the wires?
   Answer: They repel each other. This problem tests magnetism and current-carrying wires. Parallel wires carrying currents create magnetic fields that exert forces on each other according to Ampere's law. When currents flow in opposite directions (one up, one down), the wires repel each other because the magnetic field from one wire creates a force pushing the other wire away. The left wire's upward current creates a magnetic field that circles counterclockwise (viewed from above), pointing out of the page at the right wire's location, causing a rightward force on the downward current. Choice A incorrectly applies the rule for same-direction currents, confusing opposite currents with parallel currents. Remember the simple rule: parallel currents attract, antiparallel currents repel.
2. A 0.15 m wire segment is vertical and carries $I=5.0\ \text{A}$ upward. A uniform magnetic field of $0.30\ \text{T}$ points into the page. Which statement best describes the direction of the magnetic force on the segment?
   Answer: The force is to the right. This problem tests magnetism and current-carrying wires. The wire carries current upward (vertical), and the magnetic field points into the page. Using the right-hand rule: point fingers upward (current direction), curl them into the page (field direction), and the thumb points to the right. Therefore, the magnetic force on the wire segment is to the right. Choice C incorrectly suggests the force is into the page, which represents the misconception of confusing the field direction with the force direction. Always apply the right-hand rule carefully: fingers along current, curl toward field, thumb shows force.
3. A horizontal wire carries current to the west. A uniform magnetic field points downward. Which statement best describes the direction of the magnetic force on the wire?
   Answer: It points south. This problem tests magnetism and current-carrying wires. The wire carries current west (horizontal) in a downward-pointing magnetic field (vertical). Using the right-hand rule, point fingers west (current) and curl them downward (field); your thumb points south. The force is horizontal and perpendicular to both the horizontal current and vertical field. Choice A (downward) incorrectly assumes force aligns with the field direction, missing that magnetic force must be perpendicular to B. To solve efficiently, recognize that with horizontal current and vertical field, the force must be in the remaining horizontal direction.
4. A horizontal wire carries current to the right in a uniform magnetic field $\vec B$ also to the right. Which statement best describes the magnetic force on the wire?
   Answer: The force is zero. This problem tests magnetism and current-carrying wires. When current and magnetic field are parallel (both pointing right), the magnetic force is zero because F = IL × B and the cross product of parallel vectors is zero. This is a fundamental property: magnetic forces only exist when current and field have some perpendicular component. No amount of current or field strength can create a force when they're perfectly aligned. Choice A incorrectly assumes any current in a field experiences force, missing the crucial role of relative orientation. Always check if current and field are parallel before calculating forces - this saves time and prevents errors.
5. Two long parallel wires carry currents in the same direction (both upward). Which statement best describes the magnetic forces between the wires?
   Answer: They attract each other. This problem tests magnetism and current-carrying wires. Parallel wires carrying currents in the same direction attract each other due to the magnetic interaction between them. Each wire creates a circular magnetic field, and when both currents flow upward, the field from one wire at the location of the other creates an attractive force. This follows from the fundamental principle that parallel currents attract while antiparallel currents repel. Choice A incorrectly reverses this rule, possibly confusing same-direction currents with opposite-direction currents. Remember this key principle: like currents attract, unlike currents repel - opposite to electric charges.
6. A straight wire carries $2.0\ \text{A}$ upward. At a point to the right of the wire, the magnetic field due to the wire is into the page. Which statement best describes the magnetic force on a second wire at that point carrying current to the right?
   Answer: It is directed upward on the page. This problem tests understanding of magnetism and current-carrying wires. A wire carrying current upward creates a circular magnetic field around it - using the right-hand rule, if the field is into the page to the right of the wire, this confirms the upward current direction. For the second wire carrying current to the right in this field (into the page), apply the right-hand rule: fingers right (current), curl into page (field), thumb points upward (force). Choice B incorrectly assumes forces act along the wire direction, confusing magnetic force with tension or other longitudinal forces. Always determine the magnetic field first, then apply the force rule to find the perpendicular force direction.
7. A vertical wire carries current downward through a uniform magnetic field out of the page. Which statement best describes the magnetic force on the wire?
   Answer: The force is to the left. This problem tests magnetism and current-carrying wires. A vertical wire with downward current in a magnetic field out of the page experiences a force found by the right-hand rule: point fingers down (current) and curl them out of the page (field) - your thumb points left, indicating the force direction. The force is perpendicular to both the current and magnetic field, following F = IL × B. The downward current interacts with the outward field to produce a leftward force. Choice A reverses the force direction, a common error when confusing the right-hand rule steps. Practice the right-hand rule with clear finger positions: straight fingers for current, curl for field, thumb for force.
8. A straight wire carries current into the page. A uniform magnetic field points to the right. Which statement best describes the magnetic force on the wire?
   Answer: It points upward. This problem tests magnetism and current-carrying wires. The current points into the page while the magnetic field points right. Using the right-hand rule for F = IL × B, point fingers into the page (current) and curl them toward the right (field); your thumb points upward. The force is perpendicular to both the into-page current and rightward field. Choice B (into page) shows the error of thinking force aligns with current direction, missing that magnetic force is always perpendicular to I. When current is perpendicular to the page, visualize the 3D geometry carefully to apply the right-hand rule correctly.
9. A vertical wire carries current upward through a region where $\vec B$ points to the east. Which statement best describes the magnetic force on the wire?
   Answer: The force is toward the south. This problem tests magnetism and current-carrying wires. A vertical wire carrying current upward in an eastward magnetic field experiences a force determined by F = IL × B using the right-hand rule. Point your fingers upward (current direction) and curl them toward the east (field direction) - your thumb points south, indicating the force direction. The force is always perpendicular to both the current and magnetic field vectors. Choice C incorrectly assumes forces act along the wire direction, a misconception that confuses electric forces with magnetic forces. To solve magnetic force problems, visualize the three-dimensional geometry and apply the right-hand rule systematically.
10. A vertical wire carries current downward in a uniform magnetic field directed east. Which statement best describes the direction of the magnetic force on the wire?
    Answer: It points north. This problem tests magnetism and current-carrying wires. The wire carries current downward (vertical) in an eastward magnetic field (horizontal). Using the right-hand rule, point fingers downward (current) and curl them east (field); your thumb points north. The force is horizontal and perpendicular to both the vertical current and horizontal field. Choice C (downward) incorrectly assumes force aligns with current, forgetting that magnetic force must be perpendicular to both I and B. When current and field are perpendicular, the force direction completes a right-handed coordinate system with them.
11. A horizontal wire carries current to the left. It is placed in a uniform magnetic field directed out of the page. Which statement best describes the direction of the magnetic force on the wire?
    Answer: The force is upward. This problem tests magnetism and current-carrying wires. The wire carries current to the left (horizontal), and the magnetic field points out of the page. Applying the right-hand rule: point fingers left (current), curl them out of the page (field), and the thumb points upward. The force on the wire is therefore upward. Choice D incorrectly suggests downward force, which represents the misconception of using the left-hand rule or reversing the cross product. Always use the right-hand rule consistently: current × field = force direction.
12. Two long, parallel wires are 4.0 cm apart. Wire 1 carries 2.0 A upward; wire 2 carries 2.0 A upward. Which statement best describes the interaction between the wires?
    Answer: They attract because the currents are in the same direction. This problem tests magnetism and current-carrying wires. Two parallel wires both carry current upward in the same direction. When parallel currents flow in the same direction, the wires attract each other due to the magnetic fields they create. Wire 1 creates a magnetic field that circles around it (by the right-hand rule), and at the location of wire 2, this field causes a force that pulls wire 2 toward wire 1. Choice A incorrectly states they repel, which represents the misconception that same-direction currents repel like same-sign charges do. Remember that parallel currents in the same direction always attract, while opposite currents repel.
13. A straight wire carries $I$ to the right. A uniform magnetic field points to the right as well. Which statement best describes the magnetic force on the wire?
    Answer: It is zero. This problem tests magnetism and current-carrying wires. The current flows right and the magnetic field also points right, making them parallel (θ = 0°). The magnetic force formula F = ILB sin(θ) shows that when current and field are parallel, sin(0°) = 0, so the force is zero. No magnetic force acts on a current-carrying wire when current flows parallel or antiparallel to the magnetic field. Choice B (upward) represents applying the right-hand rule incorrectly when vectors are parallel, a common procedural error. Always check the angle between current and field first; if parallel or antiparallel, the force is automatically zero.
14. A straight wire carries current into the page through a region where the uniform magnetic field points to the right. Which statement best describes the magnetic force on the wire?
    Answer: It is directed downward on the page. This problem tests understanding of magnetism and current-carrying wires. When current flows into the page through a rightward-pointing magnetic field, we find the force using the right-hand rule. Point your fingers into the page (current direction) and curl them to the right (field direction) - your thumb points downward on the page. Choice D incorrectly suggests the force follows the magnetic field direction, demonstrating the misconception that forces align with fields rather than being perpendicular. Remember to visualize the three-dimensional nature of the problem and apply the right-hand rule carefully to find the perpendicular force direction.
15. A wire segment lies along the +y direction and carries $I$ upward. It is in a uniform magnetic field that points in the +y direction. Which statement best describes the magnetic force on the wire?
    Answer: The force is zero. This problem tests magnetism and current-carrying wires. The wire carries current in the +y direction (upward), and the magnetic field also points in the +y direction. When current and magnetic field are parallel (or antiparallel), the cross product I × B equals zero. Therefore, there is no magnetic force on the wire. Choice A incorrectly suggests a force in the +y direction, which represents the misconception that parallel vectors produce a force in their common direction. Remember that magnetic force requires current and field to have some perpendicular component.
16. Two long parallel horizontal wires are $6.0\ \text{cm}$ apart. The top wire carries $2.0\ \text{A}$ east; the bottom wire carries $2.0\ \text{A}$ west. Which statement best describes the force on the top wire due to the bottom wire?
    Answer: It is upward, away from the bottom wire. This problem tests magnetism and current-carrying wires. The top wire carries current east while the bottom wire carries current west, making them antiparallel. Using the right-hand rule, the bottom wire creates a magnetic field that circles it; at the top wire's location, this field points into the page. Applying F = IL × B to the top wire (current east, field into page) gives a force pointing upward, away from the bottom wire. Choice B (downward) represents the attraction misconception, forgetting that antiparallel currents repel. To avoid errors, always determine the magnetic field at one wire's location due to the other wire first.
17. A horizontal wire carries current to the right. The magnetic field at the wire is also to the right. Which statement best describes the magnetic force on the wire segment?
    Answer: It is zero because $\vec{I}$ is parallel to $\vec{B}$. This problem tests understanding of magnetism and current-carrying wires. When current and magnetic field are parallel (both to the right), the magnetic force on the wire is zero because F = IL × B involves the cross product of parallel vectors. The force magnitude is proportional to sin(θ) where θ is the angle between current and field - when θ = 0° (parallel), sin(0°) = 0, so no force exists. Choice B incorrectly applies the right-hand rule to parallel vectors, not recognizing that no perpendicular force can result from parallel current and field. Check the angle between current and field first - if parallel or antiparallel, the magnetic force is always zero.
18. A straight wire lies along the +x-axis with current to the right. The magnetic field points into the page. Which statement best describes the direction of the force on the wire?
    Answer: The force is in the +y direction. This problem tests magnetism and current-carrying wires. The wire carries current along +x (to the right), and the magnetic field points into the page (-z direction). Using the right-hand rule: point fingers right (+x), curl them into the page (-z), and the thumb points upward (+y). The force is in the +y direction. Choice B incorrectly suggests the force is into the page, confusing the field direction with the force direction. Always apply the right-hand rule systematically to find the force as the cross product of current and field.
19. A horizontal wire carries conventional current to the left through a uniform magnetic field directed upward on the page. Which statement best describes the magnetic force on the wire?
    Answer: It is directed into the page. This problem tests understanding of magnetism and current-carrying wires. When current flows to the left through an upward-pointing magnetic field, we apply the right-hand rule to find the force direction. Point your fingers left (current direction) and curl them upward (field direction) - your thumb points into the page, indicating the force direction. Choice D incorrectly assumes the force follows the magnetic field direction, a fundamental misconception about how magnetic forces work perpendicular to both current and field. Use the right-hand rule systematically: fingers along current, curl toward field, thumb shows force - the force is always perpendicular to both.
20. Two long, parallel wires are 6.0 cm apart. Wire A carries 3.0 A upward; wire B carries 3.0 A downward. Which statement best describes the magnetic force between the wires?
    Answer: They repel because the currents are in opposite directions. This problem tests magnetism and current-carrying wires. Wire A carries current upward while wire B carries current downward, making them antiparallel currents. When parallel wires carry currents in opposite directions, they repel each other. This occurs because wire A's magnetic field at wire B's location creates a force pushing B away, and vice versa. Choice B incorrectly states they attract because opposite currents attract, which confuses magnetic forces with electric charges. Remember the rule: parallel currents in the same direction attract, while antiparallel currents repel.

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