What is 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.
FAQs on Magnetic Moment
1. What is meant by magnetic moment and what is its SI unit?
The magnetic moment (or magnetic dipole moment) is a vector quantity that measures the strength and orientation of a magnet or any object that produces a magnetic field. It quantifies the tendency of the object to align with an external magnetic field. The SI unit for magnetic moment is the ampere-square meter (A·m²).
2. How is the magnetic moment of a bar magnet calculated?
The magnetic moment of a bar magnet is calculated as the product of its pole strength and its magnetic length. The formula is M = qm × 2l, where 'M' is the magnetic moment, 'qm' is the pole strength, and '2l' represents the magnetic length (the distance between the two poles). The direction of the magnetic moment vector points from the south pole to the north pole inside the magnet.
3. What is the formula for the magnetic moment of a current-carrying loop?
For a planar loop of wire carrying a steady current, the magnetic moment is given by the formula M = I × A. Here, 'I' is the current flowing through the loop, and 'A' is the area vector of the loop. The direction of the magnetic moment is perpendicular to the plane of the loop and can be determined using the right-hand thumb rule: if you curl the fingers of your right hand in the direction of the current, your thumb points in the direction of the magnetic moment.
4. Why does an electron revolving in an atom's orbit possess a magnetic moment?
An electron revolving around the nucleus constitutes a tiny electric current loop. According to the principles of electromagnetism, any moving charge or electric current creates a magnetic field. This current loop, therefore, has an associated magnetic moment called the orbital magnetic moment. Its existence is a direct consequence of the electron's charge and its orbital motion, fundamentally linking atomic structure to magnetism.
5. What is the difference between an electron's orbital magnetic moment and its spin magnetic moment?
The key difference lies in their origin:
- Orbital Magnetic Moment: This arises from the physical movement of the electron in an orbit around the nucleus. It is analogous to the magnetic moment produced by a classical current loop.
- Spin Magnetic Moment: This is an intrinsic, quantum-mechanical property of the electron itself, independent of its motion around the nucleus. It is often visualized as the electron spinning on its own axis, though this is a classical analogy. This property is as fundamental as the electron's charge or mass.
The total magnetic moment of an atom is the vector sum of the orbital and spin magnetic moments of all its electrons.
6. How does the concept of magnetic moment explain the behaviour of paramagnetic materials?
In paramagnetic materials, the atoms or molecules have a net, non-zero magnetic moment due to the presence of unpaired electrons. However, in the absence of an external magnetic field, these individual magnetic moments are randomly oriented due to thermal agitation, so the material as a whole has no net magnetisation. When an external magnetic field is applied, it exerts a torque on these atomic moments, causing them to partially align with the field, resulting in a weak magnetisation in the same direction as the external field.
7. What is the Bohr Magneton and what is its significance in physics?
The Bohr Magneton (μB) is the fundamental physical constant representing the natural unit for expressing the magnetic moment of an electron. It is defined as μB = eħ / 2me, where 'e' is the electron charge, 'ħ' is the reduced Planck constant, and 'me' is the electron mass. Its significance lies in bridging classical electromagnetism with quantum mechanics, representing the smallest possible quantum of magnetic moment that can be associated with an electron's orbital or spin angular momentum.
8. How does the magnetic moment of an object determine the torque it experiences in a magnetic field?
The torque experienced by an object with magnetic moment M when placed in a uniform external magnetic field B is given by the vector cross product: τ = M × B. The magnitude of this torque is τ = MB sin(θ), where θ is the angle between the magnetic moment vector and the magnetic field vector. This torque acts to align the magnetic moment with the direction of the external field, which is the principle behind how a compass needle works.
