## What is Magnetic Dipole Moment?

The magnetic moment is defined as the alignment of a magnet and its strength when the magnet is creating a magnetic field. There are number of examples of the magnetic moment, few are a current carrying conductor in the form of coil, elements at microscopic levels like electrons and many more.

In other simple word, the ability or a way in which a magnetic material align with the magnetic field is called as the magnetic moment. The magnetic moment is the vector quantity and the magnetic moment have a vector that is parallel to the magnetic field it is placed in. The magnetic vector goes from the south of pole to the north of pole and it is proportional to the magnetic field.

The diagram for magnetic vector is shown below:

## Production of Magnetic Moment

There are two reasons for the magnetic moment, the first one is due to the motion due to the electric charge and the other one is due to the spin angular moment.

### Measurement of Magnetic Moment

To measure the magnetic moment device used is called magnetometer. The magnetometer can determine the magnetic moment either directly or indirectly by measuring the magnetic field and then determining the magnetic moment.

Consider the formula to determine the torque for magnetic moment.

$\Gamma =mB$

Here, Γ is the torque, B is the magnetic field and m is the magnetic moment.

Consider that the magnetic moment is product of the current flowing in the loop in case of electromagnet and the area of the cross section of the loop.

M=IA

Here, I is the current and A is the area.

The unit of the magnetic moment is denoted by the ampere meter square or in joule per Tesla.

## Magnetic Dipole Moment

The magnetic dipole is defined as two poles that are separated from each other by a distance and are opposite in polarity. Consider the power of the magnetic dipole moment is m, l is the length between the poles and M is the magnetic dipole moment and is given by:

$M=\frac{m}{2l}$

The magnetic dipole moment shows the magnitude and the strength of the dipole. The dipole moment is also denoted by the torque experienced by a magnetic material due to the magnetic field. The magnetic field and the magnetic moment shares a proportional relationship. The other factors on which this dipole moment depends is the orientation of the dipole.

### Force Due to Magnetic Dipole

The magnetic dipole have two faces that have opposite polarity and the two faces are separated by a distance, so the magnetic dipole can be considered as bar magnet that has a magnetic field B.

Consider a magnetic moment m_{B} for the force on the North pole is along the magnetic filed and another magnetic moment m_{B} for the force on the south pole opposite to the magnetic field. Both the forces are opposite and produces a torque on the bar magnet such that it forms a couple and is given by.

$\tau =2mBL\mathrm{sin}\theta $

Here, the angle θ is the angle between the magnet and the magnetic field.

Consider by the formula of the dipole moment M=2mL and the magnetic dipole moment torque is of the form.

$\tau =MB\mathrm{sin}\theta $

## Relation between Magnetic Moment and Magnetization

The magnetic strength of the material is defined by the magnetic moment of the material. To determine the amount of the magnetic moment each portion of the material is capable to produced is determine the magnetization field equation.

Consider the formula for the magnetization field.

$M=\frac{dm}{dV}$

Here, m is the magnetic dipole moment and V is the volume of the portion whose magnetic moment is to be determined.

Consider the case of uniform magnetization, this is the state where the magnetization field has both the direction and magnitude equal to each other. In this case the magnetic moment follows the relation.

$m=MV$

Here, V represents the volume of the complete magnet.

## Magnetic Moment for Solenoid

Consider the case for a coil carrying current also known as solenoid. The magnetic moment of the solenoid is the product of the number of turns, current and the vector area of the solenoid.

The magnetic moment of solenoid is of the form.

$m=NIS$

The solenoid as current flows through it considered as the bar magnetic.

Consider μ as the magnetic moment, m as the pole strength and 2l is the distance between the pole. The magnetic moment is written as:

$\mu =2ml$

In terms of the current I and the area of the cross section A. The magnetic moment is of the form:

$\mu =IA$

The diagram for the illustration is shown below:

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is mainly used for

- Bachelor of Science in Physics
- Bachelor of Technology in Electrical Engineering
- Masters of Science in Physics
- Research field in physics

This concept is applied in different instruments and fields such as

- Application in Stereo-chemistry
- Application in Electric motors
- Applications in Measuring Instruments
- Applications in Loud Speakers
- Applications in Electrical Engineering

## Related Concepts

- Magnetic moment of electrons, atoms, molecules
- Magnetic field due to dipole moments
- Magnetic pole method
- Amperian loop method
- Magnetic moment relation with angular momentum

## Common Mistakes

- Check the alignment of the atoms while dealing with spin magnetic moments.
- Do not use incorrect units for the magnetic moment.
- While dealing with the measuring instruments spin moment must be considered carefully to get the precise calculation.

## Practice Problems

**Q1.** Determine the correct unit of the magnetic dipole moment.

(a) Ampere Newton

(b) Ampere meter square

(c) Ampere per square meter

(d) None of these

**Correct option:** (b)

**Explanation:** The unit for the magnetic dipole moment is ampere meter square.

**Q2. ** A solenoid can be considered as a bar magnet when____.

(a) It is not looped

(b) Voltage is applied across it.

(c) Current passes through it.

(d) None of these

**Correct option: **(c)

**Explanation:** Solenoid is considered as bar magnet when current pass through it.

**Q3.** The magnetic filed inside the magnet is _______.

(a) Infinite

(b) Zero

(c) Maximum

(d) Half of that at the poles

**Correct option:** (b)

**Explanation: **Inside the magnet the magnetic field is always zero.

**Q4.** Correction option for the device to measure the magnetic moment.

(a) Oscilloscope

(b) Sphygmometer

(c) Barometer

(d) Magnetometer

**Correct option: ** (d)

**Explanation: **The device used to measure the magnetic moment is the magnetometer.

**Q5.** Calculate the magnetic moment of a current carrying conductor with current of 2 A and the area of cross section of 2 m^{2}.

(a) 15 Am^{2}

(b) 2 Am^{2}

(c) 1 Am^{2}

(d) 4 Am^{2}

**Correct option:** (d)

**Explanation:** Calculate the magnetic moment as:

$\begin{array}{rcl}\mu & =& AI\\ & =& \left(2{\mathrm{m}}^{2}\right)\left(2\mathrm{A}\right)\\ & =& 4{\mathrm{Am}}^{2}\end{array}$

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