Solved Examples of Magnetic Dipole Moment

📚 Quick Study Guide

• 🧲 The magnetic dipole moment ($\vec{m}$) is a vector quantity that measures the strength and orientation of a magnet or other object that produces a magnetic field.
• 🔄 For a current loop, the magnitude of the magnetic dipole moment is given by $m = NIA$, where $N$ is the number of turns in the loop, $I$ is the current, and $A$ is the area of the loop.
• 🧭 The direction of the magnetic dipole moment is perpendicular to the area of the loop, determined by the right-hand rule: If you curl the fingers of your right hand in the direction of the current, your thumb points in the direction of $\vec{m}$.
• ⚛️ Atoms and molecules can also have magnetic dipole moments due to the intrinsic angular momentum (spin) of electrons and the orbital motion of electrons around the nucleus.
• 🧭 When a magnetic dipole is placed in an external magnetic field ($\vec{B}$), it experiences a torque given by $\vec{\tau} = \vec{m} \times \vec{B}$.
• ⚡ The potential energy ($U$) of a magnetic dipole in a magnetic field is given by $U = -\vec{m} \cdot \vec{B} = -mB\cos(\theta)$, where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$.

Practice Quiz

1. What is the formula for the magnitude of the magnetic dipole moment of a current loop?
   1. $m = \frac{I}{NA}$
   2. $m = NIA$
   3. $m = \frac{NA}{I}$
   4. $m = \frac{A}{NI}$
2. The direction of the magnetic dipole moment of a current loop is:
   1. Parallel to the current flow.
   2. Tangential to the loop.
   3. Perpendicular to the area of the loop, determined by the right-hand rule.
   4. Along the axis of the wire.
3. A circular loop of radius 0.1 m carries a current of 10 A. What is the magnetic dipole moment if it has 1 turn?
   1. 0.314 Am²
   2. 3.14 Am²
   3. 31.4 Am²
   4. 0.0314 Am²
4. What is the torque on a magnetic dipole in a uniform magnetic field when the dipole moment is aligned parallel to the field?
   1. Maximum
   2. Zero
   3. Half the maximum
   4. Equal to the magnetic field strength
5. The potential energy of a magnetic dipole in a uniform magnetic field is minimum when:
   1. The dipole moment is perpendicular to the field.
   2. The dipole moment is anti-parallel to the field.
   3. The dipole moment is parallel to the field.
   4. The dipole moment is at 45 degrees to the field.
6. A coil has 100 turns and an area of 0.01 m². If a current of 2 A flows through it, what is its magnetic dipole moment?
   1. 0.2 Am²
   2. 2 Am²
   3. 20 Am²
   4. 200 Am²
7. The magnetic dipole moment is a ________ quantity.
   1. Scalar
   2. Vector
   3. Tensor
   4. Dimensionless