Magnetic Moment- Physics

What is Magnetic Moment?

The production of a magnetic field (by a magnet) using its magnetic strength and orientation properties is called magnetic moment—the magnetic moment inside the magnet points toward its north pole. The SI unit of magnetic moment is ampere-square metre (Am²). These are the same dimensions that current×area or energy/magnetic flux density has.

Magnetometers measure the magnetic moment of any magnetic material. Since the effective magnetic moment is independent of temperature and outside field strength, it is more convenient to measure than the regular magnetic moment. This study material for magnetic moment aims to simplify the concept through examples.

Mathematically speaking, the magnetic moment of the current loop can be calculated as the product of the area of the rectangular loop and the current flowing in the loop. The formula is as follows:

m = IA

Here, A is the vector quantity with the magnitude same as the area of the rectangular loop; however, its directions are given by using the right-hand thumb rule. The torque exerted on a current-carrying coil placed in a magnetic field can be given by the magnetic field and the magnetic moment’s vector product. 

τ = m x B

The Equation for the Magnetic Moment

• The equation of the magnetic moment is 

         m = IA

• The torque of the magnetic dipole moment is given by 

τ = m x B

Where B is the magnetic field.

•  The potential energy is represented as U(θ)= – m×B

Types of Magnetic Moments

1. Movement of electrons (Electric Charge)
2. Spin Angular momentum

Electronic Magnetic Moment

The intrinsic properties of spin and electric charge cause the magnetic moment in electrons. We call it the electron magnetic moment. The value of m for electrons is -9.284764×10-24 J/T.

Magnetic Dipole

When a very small distance separates two unlike magnetic poles having the same pole strengths, the arrangement is called a magnetic dipole. They are associated with the angular momentum of the body.

The torque acting on a magnetic dipole: mB sinθ

Magnetic Dipole Moment

When the total distance between the poles and their pole strength is multiplied, we get the magnetic dipole moment whose unit is joule/tesla.

The Magnetic Dipole Moment of a Current Loop

The magnetic dipole moment of a current loop carrying current I with area A is given as the magnitude of m: |m| = IA

An Atom’s Behaviour as a Magnetic Dipole

In a closed orbit, electrons in the atom revolve around the nucleus. The orbit around the nucleus is equivalent to a current loop as the electrons are charged particles. The current revolves clockwise, whereas the electrons revolve in an anticlockwise direction. This electron movement creates a north and a south pole resulting in the atom’s behaviour as the magnetic dipole. 

Magnetic Permeability Materials

Based on a material’s permeability, it is classified into the following subcategories: 

• Diamagnetism

Materials with diamagnetism have a relative permeability value slightly lesser than 1, resulting in the reduction of the magnetic flux density inside materials with diamagnetism. These materials tend to repel in external magnetic fields feebly.

Example: Bismuth, copper, gold, antimony, silver, lead, silicon, mercury

• Paramagnetism

Materials having paramagnetism have a relative permeability value slightly bigger than 1, and this is the reason why paramagnetic materials get feebly magnetic in the magnetic field’s direction when brought in contact with an external magnetic field. 

All paramagnetic atoms have a permanent magnetic dipole moment. This is because the electrons in an atom with paramagnetism spin tend to orient magnetic moments. However, if there is a thermal motion around the atom, these magnetic orientations due to the electron spinning can also be random. Due to this randomness in orientation in thermal energy, these materials have net magnetic moment zero. 

Example: Platinum, calcium, lithium, tungsten, aluminium

Ferromagnetism

Ferromagnetism is caused by the alignment of permanent dipoles in atoms that result from unpaired electrons in outer shells and the interaction between the dipoles of neighbouring atoms. For example, the outermost shell of ferromagnetic materials like iron and cobalt contains electrons, but the inner shell close to the extreme is still empty. As a result, ferroelectric materials have enormous spin magnetic moments due to their electronic structure, leading to atomic solid dipole moments.

Calculation of Magnetic Moment

For calculating the magnetic moment in Current carrying circular loop of radius R and length l:

B= µ0iR²/2(R² + l²)

For calculating the magnetic moment of an electron making revolutions: 

It is the vector sum of its orbital and spin Magnetic Moment.

             B = neh/ 4πm

Here n is a natural number 

 h is Planck’s constant.

e: charge on an electron

m = mass of electron

Explanation:

The magnetic moment of an atom is given by: 

B = ½ eωr²

e: charge on an electron

ω: Angular velocity of an electron

r: radius

Conclusion

This article about the magnetic moment discusses the critical topics covered under or related to the magnetic moment, such as its types, calculation, and variations. The study material and notes on magnetic moments are provided above. 

Herein, we define the magnetic moment as a factor to measure the tendency of a body to interact with any external magnetic field. Its direction is found by applying the right-hand thumb rule. Moving charges and spin angular momentum causes the magnetic moment to occur. The magnetic moment has three types: Para magnetism, Diamagnetism and Ferromagnetism, extensively discussed above.