AP Physics C Questions: Magnetic Force on a Current-Carrying Wire

📚 Quick Study Guide

• 𧮄 Magnetic Force: A current-carrying wire experiences a force when placed in a magnetic field.
• 📐 Formula: The magnetic force $\vec{F}$ on a straight wire of length $l$ carrying current $I$ in a uniform magnetic field $\vec{B}$ is given by $\vec{F} = I(\vec{l} \times \vec{B})$.
• 🧭 Magnitude: The magnitude of the force is $F = IlB\sin(\theta)$, where $\theta$ is the angle between the wire and the magnetic field.
• 🖐️ Right-Hand Rule: Use the right-hand rule to determine the direction of the force. Point your fingers in the direction of the current, curl them toward the direction of the magnetic field, and your thumb points in the direction of the force.
• 🔄 Force on a Curved Wire: For a curved wire, you can integrate the force over infinitesimal segments, or consider the effective straight-line distance between the endpoints.
• 💪 Maximum Force: The maximum force occurs when the wire is perpendicular to the magnetic field ($\theta = 90^\circ$), so $F_{max} = IlB$.
• 🚫 Zero Force: The force is zero when the wire is parallel to the magnetic field ($\theta = 0^\circ$ or $\theta = 180^\circ$).

Practice Quiz

1. A straight wire of length 0.5 m carries a current of 2 A perpendicular to a uniform magnetic field of 0.4 T. What is the magnitude of the magnetic force on the wire?
   1. 0.2 N
   2. 0.4 N
   3. 0.8 N
   4. 1.6 N
2. A wire carrying a current of 5 A is oriented at an angle of 30° to a magnetic field of 0.6 T. If the force on the wire is 0.3 N, what is the length of the wire?
   1. 0.1 m
   2. 0.2 m
   3. 0.3 m
   4. 0.4 m
3. A wire of length 1 m carrying a current of 3 A is placed in a magnetic field. The magnetic force on the wire is found to be maximum when the wire is perpendicular to the field. If the magnetic field is 0.5 T, what is the magnitude of the maximum force?
   1. 0.5 N
   2. 1.0 N
   3. 1.5 N
   4. 2.0 N
4. A current-carrying wire is placed parallel to a magnetic field. What is the magnetic force on the wire?
   1. Maximum
   2. Minimum
   3. Zero
   4. Cannot be determined
5. A wire of length 2 m carrying a current of 4 A is in a magnetic field of 0.7 T. If the magnetic force on the wire is 4 N, what is the angle between the wire and the magnetic field?
   1. 30°
   2. 45°
   3. 60°
   4. 90°
6. A circular loop of wire with radius 0.1 m carries a current of 2 A in a uniform magnetic field of 0.5 T. If the plane of the loop is parallel to the magnetic field, what is the net force on the loop?
   1. 0 N
   2. 0.1 N
   3. 0.2 N
   4. 0.3 N
7. What is the effect on the magnetic force if both the current in the wire and the magnetic field strength are doubled?
   1. The force remains the same.
   2. The force is halved.
   3. The force is doubled.
   4. The force is quadrupled.