Torque on a Current Loop Quiz: Test Your Knowledge

📚 Quick Study Guide

🔍 Magnetic Dipole Moment: The magnetic dipole moment ($\vec{\mu}$) of a current loop is defined as the product of the current ($I$) and the area vector ($\vec{A}$) of the loop: $\vec{\mu} = I\vec{A}$. 💡 Torque on a Current Loop: The torque ($\vec{\tau}$) on a current loop in a magnetic field ($\vec{B}$) is given by $\vec{\tau} = \vec{\mu} \times \vec{B}$. 📝 Magnitude of Torque: The magnitude of the torque is $\tau = \mu B \sin(\theta)$, where $\theta$ is the angle between the magnetic dipole moment and the magnetic field. ⚛️ Direction of Torque: The direction of the torque is perpendicular to both the magnetic dipole moment and the magnetic field, as determined by the right-hand rule. ⚗️ Units: Torque is measured in Newton-meters (N⋅m), magnetic field in Tesla (T), magnetic dipole moment in Ampere-meters squared (A⋅m²). 📊 Maximum Torque: Maximum torque occurs when the magnetic dipole moment is perpendicular to the magnetic field ($\theta = 90^\circ$), so $\tau_{max} = \mu B$. 🧠 Zero Torque: Zero torque occurs when the magnetic dipole moment is parallel or antiparallel to the magnetic field ($\theta = 0^\circ$ or $180^\circ$).

🧪 Practice Quiz

1. A circular current loop has a radius of 5 cm and carries a current of 2 A. It is placed in a uniform magnetic field of 0.5 T. What is the magnetic dipole moment of the loop?
   1. 0.0157 A⋅m²
   2. 0.0079 A⋅m²
   3. 0.157 A⋅m²
   4. 0.0314 A⋅m²
2. A square current loop with sides of 10 cm carries a current of 3 A. If it is placed in a 0.8 T magnetic field at an angle of 30 degrees to the field, what is the magnitude of the torque on the loop?
   1. 0.012 N⋅m
   2. 0.024 N⋅m
   3. 0.006 N⋅m
   4. 0.48 N⋅m
3. The torque on a current loop in a magnetic field is maximum when the angle between the magnetic dipole moment and the magnetic field is:
   1. 0 degrees
   2. 45 degrees
   3. 90 degrees
   4. 180 degrees
4. A current loop is placed in a magnetic field. Under what condition will the torque on the loop be zero?
   1. When the magnetic field is very strong
   2. When the current in the loop is zero
   3. When the area of the loop is very small
   4. When the magnetic dipole moment is perpendicular to the magnetic field
5. A rectangular loop of wire with dimensions 8 cm x 12 cm carries a current of 5 A. It's placed in a magnetic field of 0.6 T. Calculate the maximum torque on the loop.
   1. 0.0288 N⋅m
   2. 0.288 N⋅m
   3. 0.00288 N⋅m
   4. 2.88 N⋅m
6. A coil with 20 turns and an area of 0.05 m² carries a current of 4 A. It is placed in a uniform magnetic field of 0.2 T. What is the maximum torque on the coil?
   1. 0.08 N⋅m
   2. 0.8 N⋅m
   3. 0.008 N⋅m
   4. 8 N⋅m
7. If the magnetic dipole moment of a current loop is doubled and the magnetic field is halved, what happens to the torque on the loop?
   1. The torque remains the same
   2. The torque is doubled
   3. The torque is halved
   4. The torque is quadrupled