Magnetic Dipole Moment Formula and Right Hand Rule with Solved Questions
The magnetic dipole moment is a fundamental concept in magnetism that helps describe the strength and orientation of a magnet or a current-carrying loop. It plays a key role in understanding how magnets interact with external magnetic fields and how torque is generated when a magnetic material is placed within such a field. This concept is crucial for students studying Physics as it connects theoretical definition, mathematical expression, and physical significance.
Definition of Magnetic Dipole Moment
The magnetic dipole moment of a magnet is defined as the product of the pole strength and the distance between two poles. If m is the strength of each magnetic pole and 2l is the separation between them, the magnetic dipole moment (→M) is given by:
- →M = m (2⇄l)
Here, the vector is directed from the south pole to the north pole of the magnet. The magnetic dipole moment is a vector quantity, showing both magnitude and direction.
SI Units of Magnetic Dipole Moment
The SI unit of magnetic dipole moment is ampere square metre (A m2) or equivalently, joule per tesla (J T−1). These units express the product of electric current and area, or energy per unit magnetic field strength.
Magnetic Dipole Moment and Torque in a Magnetic Field
When a bar magnet (with magnetic moment M) is placed in a uniform magnetic field B, it experiences a torque. The forces on the north and south poles are equal in magnitude but opposite in direction, acting at different points and forming a couple. This results in a tendency to rotate the magnet.
Let the length of the magnet be 2l, and θ be the angle between the axis of the magnet and the magnetic field direction.
- Force on North pole = mB (along the direction of →B)
- Force on South pole = mB (opposite to →B)
These forces act at a distance to generate torque:
- ι = mB × NA
Where NA is the perpendicular distance, derived from the geometry of the magnet and the applied field:
- NA = 2l sinθ
So, the torque equation becomes:
- ι = mB × 2l sinθ = (m × 2l) B sinθ = MB sinθ
- In vector form: →ι = →M × →B
The direction of the torque is perpendicular to both the magnetic moment and the magnetic field.
Key Formulas Related to Magnetic Dipole Moment
| Quantity | Formula | SI Unit | Direction |
|---|---|---|---|
| Magnetic Dipole Moment of a Bar Magnet | M = m × 2l | A m2 or J T–1 | South to North pole |
| Torque on a Magnet in Uniform B | ι = MB sinθ (Vector: →ι = →M × →B) |
N m | Perpendicular to →M and →B |
Step-by-Step: Calculating Torque on a Magnetic Dipole
| Step | Action | Explanation |
|---|---|---|
| 1 | Identify magnetic pole strength (m) and pole separation (2l). | Given in problem or measured. |
| 2 | Calculate magnetic dipole moment (M). | Use M = m × 2l. |
| 3 | Note the uniform magnetic field (B) and angle θ. | Directions must be considered. |
| 4 | Compute torque. | Use ι = MB sinθ. |
Example Problem
Suppose a bar magnet has a pole strength of 0.5 A·m, and the distance between its poles is 4 cm. It is placed in a uniform magnetic field of 0.2 T at an angle of 30° to the field.
- Magnetic dipole moment, M = 0.5 × 0.04 = 0.02 A·m2
- Torque, ι = MB sinθ = 0.02 × 0.2 × sin30° = 0.02 × 0.2 × 0.5 = 0.002 N·m
Comparison Table: Magnetic Dipole Moment and Related Quantities
| Parameter | Magnetic Dipole Moment | Torque in Field |
|---|---|---|
| Formula | M = m × 2l | ι = MB sinθ |
| Unit | A m2 | N m |
| Nature | Vector (South to North) | Vector (⟂ to M and B) |
Key Points for Students
- The magnetic dipole moment indicates how strongly a magnet or coil can align with an external magnetic field.
- It is always directed from the south pole to the north pole inside the magnet.
- The torque experienced by a magnet in a magnetic field depends on its dipole moment, the field strength, and the angle between them.
- Always express your answers using proper SI units for clarity and consistency.
Related Vedantu Physics Resources
- Magnetic Dipole Moment (Concepts & Formulas)
- Magnetic Field (Concepts & Applications)
- Magnetization and Intensity
- Magnetic Field Due to Current Loop
- Magnetic Properties of Matter
Practice and Next Steps
- Work through practice problems on calculating magnetic dipole moment and torque.
- Review related topics like Magnets and Types and Magnetization Effects.
- Test understanding with Vedantu's topic quizzes to master both calculation and conceptual parts of magnetism.
FAQs on Magnetic Dipole Moment Explained for Class 12 & Competitive Exams
1. Define magnetic dipole moment of a magnet and write its units by taking into consideration the torque acting upon it when placed in a magnetic field.
Magnetic dipole moment of a magnet is defined as the product of its pole strength (m) and the distance (2l) between its two poles. When placed in a uniform magnetic field, the torque acting on the magnet aligns it with the field. If \( \mathbf{M} = m \times 2\mathbf{l} \), then the SI unit of magnetic dipole moment is ampere metre squared (A·m2) or joule per tesla (J·T–1). The magnetic dipole moment is a vector, directed from the south pole to the north pole.
2. What is the magnetic dipole moment of a magnet? State its unit.
Magnetic dipole moment (M) of a magnet quantifies the strength of a magnet and its ability to align with an external magnetic field. It is given by M = m × 2l, where m is pole strength and 2l is the distance between poles. The SI unit is A·m2 (ampere-metre squared) or J·T–1 (joule per tesla).
3. The torque acting on a magnetic dipole of moment P(m) when placed in a magnetic field is
The torque (τ) acting on a magnetic dipole of moment P(m) in a uniform magnetic field B is:
• τ = P(m) × B
• Magnitude: τ = P(m) B sinθ, where θ is the angle between dipole moment and the field.
• The torque tends to rotate the dipole to align with the field direction.
4. The torque acting on a magnet of magnetic moment 'M' placed in a uniform magnetic field B is
The torque (τ) on a magnet of magnetic moment M in a uniform field B is given by:
• τ = M × B
• Magnitude: τ = MB sinθ
• Here, θ is the angle between M and B. Torque is maximum when θ = 90°.
5. A magnetic dipole of moment M is placed in uniform magnetic field B so that angle between direction of M and B is θ, the torque acting on the magnetic dipole is
The torque (τ) acting is given by:
• τ = MB sinθ
• Vector form: τ = M × B
• Direction of τ is perpendicular to the plane containing M and B.
6. Define magnetic dipole moment. What are its units? Is it a scalar or a vector?
Magnetic dipole moment is a physical quantity representing the strength and orientation of a magnet or current loop. Its SI unit is ampere metre squared (A·m2) or joule per tesla (J·T–1). Magnetic dipole moment is a vector quantity, pointing from the south to the north pole for a bar magnet.
7. What is the formula for the magnetic dipole moment of a current loop?
The magnetic dipole moment (μ) of a current loop is:
• μ = I × A
• Where I = current (in amperes), A = area vector (in m2, direction given by the right-hand rule).
• The unit is A·m2.
8. What is the difference between magnetic moment and magnetic dipole moment?
Magnetic moment and magnetic dipole moment terms are often used interchangeably. In most contexts, both refer to the same quantity: the measure of a system's strength and orientation in a magnetic field (symbol: μ or M). Both are vector quantities with SI unit A·m2. The term 'dipole moment' emphasizes the system behaves like a magnet with two poles.
9. What is the right hand rule for magnetic dipole moment direction?
The right-hand rule for magnetic dipole moment states:
• Curl your fingers in the direction of conventional current in the loop.
• Your extended thumb points in the direction of the magnetic dipole moment (μ), perpendicular to the plane of the loop.
This determines the direction of the area vector and μ.
10. State two applications of magnetic dipole moment in daily life or technology.
Applications of magnetic dipole moment include:
• Bar Magnets: Used in compasses to indicate Earth's magnetic field direction.
• Electric Motors & Generators: Operating principle involves torque on magnetic dipoles created by current loops.
• MRI (Medical Imaging): Relies on spin magnetic dipole moments of nuclei/vectors.
11. What is the SI unit and dimensional formula of magnetic dipole moment?
SI unit: Ampere metre squared (A·m2) or Joule per Tesla (J·T–1).
Dimensional formula: [A][L]2 or [M0 L2 T0 A1].
12. How is the magnetic dipole moment of an electron in the Bohr model defined?
The magnetic dipole moment of an electron in the Bohr model (Bohr magneton) is:
• μB = eħ/(2me)
• Where e = charge of electron, ħ = reduced Planck's constant, and me = electron mass.
• Value: μB ≈ 9.274 × 10–24 A·m2.
