Magnetic Moment

Magnetic moment, which is also known as magnetic dipole moment, is the quantitative measure of the tendency of an object to align with a magnetic field. In other words, the magnetic moment can be described as the magnetic strength and orientation of a magnet or other object that produces a magnetic field. 

The magnetic moment can be generated using two methods which are the motion of the electric charge method and the spin angular momentum method. The magnetic moment of an object is typically measured by an instrument known as the magnetometer.

The magnetic moment is a vector quantity that has dimension [IL2]. The SI unit of magnetic dipole moment is Am2, while the CGS unit is emucm2. The relationship between these two quantities can be defined as 1 emucm2 = 10-3 Am2

Pole Strength of a Magnet

The pole strength of any magnet can be defined as the Force with which material gets attracted towards the magnet. Pole strength is a vector quantity. The magnetic moment of an object is the product of pole strength and the length of the magnet. 

Since pole strength and magnetic moment are directly related, the force on the north pole of the magnet points towards a magnetic field B and the force on the south pole of the magnet is opposite to that. Both the forces have a magnitude F. 

The moment of a couple (i.e. torque) is given by,

N = F × r

The direction of the torque is perpendicular to the plane of the paper and its magnitude is given by,

N = F r sinθ 

Considering the magnetic moment of the bar magnet to be m, the torque has a magnitude,

N = mBsinθ

Comparing the expressions,

F r sinθ  = mBsinθ

The quantity

F= \[\frac{mB}{r}\]

is equivalent to electric charge and it is referred to as the “pole strength”. The strength of north pole is taken to be +qm and that of south pole is chosen as -qm.

qm=\[\frac{m}{r}\]

According to the pole strength formula, the pole strength of a magnet is given by the ratio of magnetic moment to its effective length (called the magnetic length). SI unit of pole strength is A . m.

Force and Potential Energy

The force on a magnetic moment m due to a magnetic field B is given by,

F = (m . ▽)B

The potential energy is as follows,

U = -m . B

Magnetic Moment in Chemistry

An electron revolving around the nucleus of an atom, constitutes a closed current-carrying loop. The magnetic moment of an electron is,

m = \[-\frac{\mu g}{h}L\]

Here, L is the angular momentum and it is quantized in units of Planck’s constant ħ.

is called Bohr magneton defined as,

μB = \[\frac{e\hbar}{2m_e}\]

Here, the mass of an electron, me = 9.1×10−31kg 

Charge of an electron, e = 1.6×10−19C 

Planck’s constant, h= 2πℏ = 6.626×10−34J.s.

The magnetic moment due to the orbital motion of an electron (with orbital quantum number l) as a magnitude is given by,

ml = \[\sqrt{l(l+1){\mu _B}}\]

Apart from this, an electron has a magnetic moment due to its intrinsic spin (s=1/2). It has a magnitude given by the spin magnetic moment formula,

Ms = \[2\sqrt{s(s+1){\mu _B}}\]

Protons and neutrons are spin half (s = 1/2) particles. The magnetic moments have magnitudes.

Mp = \[g_p\sqrt{s(s+1)}\frac{e\hbar}{2M_p}\]

Mn = \[g_n\sqrt{s(s+1)}\frac{e\hbar}{2M_n}\]

Here, Mp and Mn are the masses of protons and neutrons respectively, and gp and gn are empirical constants. 

Did You Know?

• Materials, consisting of atoms with unpaired electrons are called paramagnetic. Each atom behaves as a tiny dipole moment. Normally, they remain randomly oriented. But in the presence of an external magnetic field, the dipoles tend to get arranged parallel to the magnetic field.

• Total magnetic moment of an electron is a sum of orbital and spin magnetic moments. 

• Magnetic moment of an electron is opposite to its angular momentum. Like angular momentum and spin, magnetic moment is also quantized.

• Ferromagnetic atoms have a much higher value of magnetic moment than that of paramagnetic atoms.

• Most of the paramagnetic materials are colored.

• Early theories concerning magnetostatics considered the existence of magnetic monopoles. But Gauss’ law discards the concept of monopoles.

• Magnetic field strength at a point, due to a magnetic moment, is inversely proportional to the cube of the distance of that point from the dipole.