Solved Examples of Magnetic Force on a Current-Carrying Wire

📚 Quick Study Guide

• 🧲 The magnetic force on a current-carrying wire is given by $\vec{F} = I \vec{L} \times \vec{B}$, where $I$ is the current, $\vec{L}$ is the length vector of the wire, and $\vec{B}$ is the magnetic field.
• 📐 The magnitude of the force is $F = I L B \sin(\theta)$, where $\theta$ is the angle between the wire and the magnetic field.
• 🖐️ Use the right-hand rule to determine the direction of the force: point your fingers in the direction of the current, curl them towards the magnetic field, and your thumb points in the direction of the force.
• 🧭 The direction of $\vec{L}$ is the direction of the current.
• 💡 If the wire is not straight or the magnetic field is not uniform, you may need to integrate over the length of the wire to find the total force: $\vec{F} = \int I d\vec{L} \times \vec{B}$.

Practice Quiz

1. What is the magnetic force on a 1.0 m long wire carrying a current of 5.0 A perpendicular to a uniform magnetic field of 0.20 T?
   1. 0.10 N
   2. 1.0 N
   3. 0.0 N
   4. 2.5 N
2. A wire carrying a current of 3.0 A is placed at an angle of 30 degrees to a magnetic field of 0.3 T. If the wire is 0.5 m long, what is the magnitude of the magnetic force on the wire?
   1. 0.225 N
   2. 0.45 N
   3. 0.9 N
   4. 0.15 N
3. A straight wire of length 0.2 m carries a current of 4 A in the positive x-direction. There is a magnetic field of 0.5 T in the positive z-direction. What is the direction of the magnetic force on the wire?
   1. Positive x-direction
   2. Negative x-direction
   3. Positive y-direction
   4. Negative y-direction
4. A wire carrying a current of 2 A is in a magnetic field. The force on the wire is 1 N, and the length of the wire in the field is 0.5 m. What is the magnetic field strength if the wire is perpendicular to the field?
   1. 0.25 T
   2. 1.0 T
   3. 4.0 T
   4. 0.5 T
5. If a wire carrying current is parallel to the magnetic field, what is the magnetic force on the wire?
   1. Maximum
   2. Zero
   3. Half the maximum force
   4. Cannot be determined
6. A 2.0 m wire carrying a 7.0 A current has a magnetic force of 0.08 N acting on it when placed in a uniform magnetic field. If the angle between the wire and the magnetic field is 90°, what is the magnitude of the magnetic field?
   1. 0.0057 T
   2. 0.057 T
   3. 0.011 T
   4. 0.00057 T
7. A circular loop of wire carrying current is placed in a uniform magnetic field. What is the net force on the loop?
   1. Maximum
   2. Zero
   3. Depends on the direction of the current
   4. Depends on the radius of the loop