## What is Magnetic Moment?

The** magnetic moment**Â is a determination of its tendency to get arranged through a magnetic field. As we all know, a magnet has two poles, i.e., **North**Â andÂ **South**.

*Magnetic moment can be defined as:*

The magnetic strength and orientation of a magnet or other object that produces a magnetic field.

**Examples of objects having magnetic moments:**

- Permanent magnets
- Astronomical objects.
- Loops of electric current
- Various molecules
- Elementary particles

### Magnetic Moment Formula:

The magnetic moment is a vector relating torque of an object to the magnetic field. This is mathematically represented as:

Ï„ = mÂ Ă— B |

*Where,*

- Ï„ is the torque acting on the dipole
- m is the magnetic moment
- B is the external magnetic field

### Magnetic Moment Unit:

In the definition for the current loop, the Magnetic moment is the product of the current flowing and the area,Â **M = I A**

- So the unit conferring to this definition is articulated byÂ
**Amp-m**.^{2} - It can also be suggested in terms of torque and moment. Conferring to that,Â the torque is measured in JoulesÂ
**(J)**Â and the magnetic field is measured in teslaÂ**(T)**Â and thus the unit isÂ**J TÂ**.^{-1} - So, these two units are equivalent to each other and are provided by
**Â 1 Amp-m**^{2}Â = 1 J T^{Â -1}.

**Related Articles:**

## What is Magnetic Dipole Moment?

A Magnetic Dipole comprises two unlike poles of equivalent strength and parted by a small distance.

**For instance:** The needle of a compass, a bar magnet, etc. are magnetic dipoles. We shall show that a current loop works as a magnetic dipole.

Magnetic Dipole Moment is described as the product of pole strength and the distance amidst the two poles. The distance between the two poles of a magnetic or a magnetic dipole is named as the magnet length and is given as the 2Â Î¹.

**IfÂ mÂ is the power of any magnetic pole then the magnetic dipole moment of the magnet is signified by the vectorÂ M and it is represented as**

**The Magnetic dipole moment is a vector and it has a direction from the South Pole of the magnet to the north pole of the magnet, as presented in the figure**

**Magnetic Dipole Moment**

### Expression for Magnetic Dipole Force:

The force on a magnetic dipole is because of both the poles of the magnet, and we consider the magnetic dipole of a bar magnet and assume that the magnet is kept in an unbroken magnetic fieldÂ **B**. In that situation, the force on the separate poles is articulated as

**m**Â which is along with the magnetic fieldÂ_{B}**B**=Â Force on the N-pole**m**Â and this is opposite to magnetic fieldÂ_{B}**B**= Force on the S-pole

These forces are equivalent in magnitude, but opposite in direction and they form a parallel couple that rotates the magnet clockwise and creates a net torque on the magnet because of the individual force in a couple; thus we have torque acting on the bar magnet.

**Ï„Â **= Moment of the couple.

**Ï„Â **= m_{B}Â Ă—Â 2L sinÂ Î¸

WhereÂ Î¸Â is the angle amid the magnet and the magnetic field, therefore, from the above discussion we have

**M** = m x 2L

Thus, Magnetic dipole moment is articulated by

**Ï„Ï„**Â = MB sinÂ Î¸

In vector form, it can be rephrased as:

Ï„Â = MÂ Ă—Â B |

This is the required expression for the **magnetic dipole force**.

## Magnetic Moment Questions

### What is theÂ magnetic moment spin formula?

Following is the magnetic moment spin formula:

\(\sqrt{n(n+2)}\) |

Where n is the number of unpaired electrons.

### What is the magnetic moment of Mn2+ ion?

Mn2+ ion has 5 unpaired electrons. By using magnetic moment for spin formula \(\sqrt{n(n+2)}\), where n is 5. We get the magnetic moment of Mn2+ as 5.96.

### What is the magnetic moment of Ni2+ ion?

Ni2+ ion has 2 unpaired electrons. By using magnetic moment for spin formula \(\sqrt{n(n+2)}\), where n is 2. We get the magnetic moment of Ni2+ as 2.8.

### What is the magnetic moment of a bar magnet?

Consider a bar magnet of length l and with magnetic moment m. Bend the bar magnet in the form of a semicircular magnet, then the new magnetic moment will be:

\(m’=\frac{2m}{\pi }\) |

### What is the magnetic moment of electron?

An electron has a magnetic moment due to its orbital motion and is given as:

\(\frac{\mu _{B}}{2 }\) |

*If you wish to learn moreÂ about the magnetic moment with the help of interactive video lessons, download BYJU’S – The Learning App.*