Revision: Magnetic Materials Physics HSC Science (General) 12th Standard Board Exam Maharashtra State Board

The product of pole strength and magnetic length of a magnetic dipole, which represents the strength of a magnet, is called its magnetic dipole moment.

The work done in rotating a magnetic dipole against the action of the torque in a uniform magnetic field, which is stored in the dipole, is called the magnetic potential energy of the dipole.

The magnetic moment of an electron revolving around the nucleus of an atom, arising due to its orbital motion similar to a tiny current loop, is called the orbital magnetic moment of the electron.

The ratio of magnetic moment to the volume of the material is called magnetization.

The ratio of the magnitude of total field inside the material to that of intensity of magnetising field is called magnetic permeability.

The ratio of magnetic moment to the volume of the material is called magnetisation.

The ratio of the strength of the magnetizing field to the permeability of free space is called magnetic intensity. 

The magnetic moment developed per unit volume of a material when placed in a magnetising field is called intensity of magnetisation.

The ability of magnetising field to magnetise a material medium is called magnetising field intensity.

The total magnetic field inside a magnetic material, which is the sum of the external magnetising field and the additional magnetic field produced due to magnetisation of the material, is called magnetic induction.

The magnetic field that exists in vacuum and induces magnetism is called magnetising field.

The ratio of magnetic permeability of the material (μ) and magnetic permeability of free space (μ₀) is called relative permeability.

The ratio of the strength of magnetising field to the permeability of free space is called magnetic intensity.

The ratio of magnitude of intensity of magnetisation to that of magnetic intensity is called magnetic susceptibility.

The residual value of magnetic induction (B) retained by a ferromagnetic material when the magnetising field (H) is reduced to zero (represented by point B/C on the hysteresis loop) is called retentivity.

The lagging of intensity of magnetisation (I) or magnetic induction (B) behind the magnetising field (H) during the process of magnetisation and demagnetisation of a ferromagnetic material is called hysteresis.

The value of the reverse magnetising field (H₀) required to reduce the residual magnetic induction of a ferromagnetic material to zero (represented by point F on the hysteresis loop) is called coercivity.

Substances which at room temperature retain their ferromagnetic property for a long period of time are called permanent magnets.

A material whose atoms or molecules possess permanent magnetic dipole moments and exhibit strong magnetic properties due to alignment of these moments is called a ferromagnetic material.

The property by which a material is weakly attracted towards an external magnetic field and moves from weaker region to stronger region of the field is called paramagnetism.

A material whose atoms or molecules possess permanent magnetic dipole moments due to unpaired electrons but have zero net magnetic moment in the absence of an external magnetic field is called a paramagnetic material.

The magnetic field produced inside a solenoid due to current flowing through it, independent of the material placed inside, is called magnetic field intensity (H).

H = nI

A material whose atoms or molecules have completely filled electron orbits and hence possess no net magnetic dipole moment is called a diamagnetic material.

The ratio of a material's net magnetic moment to its volume is called magnetisation.

M = \[\frac{\text{Net magnetic moment}}{\mathrm{Volume}}\]

The phenomenon of complete expulsion of magnetic field lines from a superconductor when placed in an external magnetic field is called the Meissner effect.

The property by which a material is weakly repelled by an external magnetic field and moves from stronger to weaker region of the field is called diamagnetism.

The property of a material which indicates how easily magnetic field lines pass through it is called magnetic permeability (μ).

μ = μ₀(1 + χ)

The strong interaction between neighbouring atomic magnetic dipole moments that causes their parallel alignment in a domain is called exchange interaction.

The phenomenon in which magnetic field lines are diverted through a soft ferromagnetic material so that very few lines pass through the enclosed space is called magnetic shielding.

The value of the magnetising field H required to reduce the magnetic flux density B to zero is called coercivity.

The value of magnetic flux density B remaining in a material when the magnetising field H is reduced to zero is called retentivity (or remanence).

The closed curve obtained when a ferromagnetic material is taken through one complete cycle of magnetisation is called a hysteresis loop.

The ratio of magnetic permeability of a material to the permeability of free space is called relative magnetic permeability (μr).

μ_r = 1 + χ

The ratio of magnetisation produced in a material to the applied magnetic field intensity is called magnetic susceptibility (χ).

M = _χH

It is the ratio of magnetic moment to angular momentum.

Gyromagnetic ratio = \[\frac {e}{2m_e}\]

T = \[\frac {2π}{ω}\] = 2π\[\sqrt {\frac {1}{mB}}\]

• Scalar form: τ = mB sin ⁡θ
• Vector form (rectangular current-carrying coil in uniform field): \[\vec τ\] = \[\vec M\] × \[\vec B\]

m_orb​ = IA

For an electron revolving in a circular orbit:

m_orb​ = \[\frac {evr}{2}\]

T = \[2\pi\sqrt{\frac{I}{mB}}\]

B = μ₀​(1 + χ)H

τ = m × B

Magnitude:

τ = m B sin θ

U = −m B cos θ

If a magnetic dipole is rotated against the action of the torque in a uniform magnetic field, work has to be done. This work is stored as the potential energy of the dipole and is given by U = −\[\vec M\] . \[\vec B\] = −mB cos ⁡θ.
Special cases:

• At θ = 0° (M parallel to B): U_min = −mB → bar magnet is in stable equilibrium with minimum potential energy.
• At θ = 90° (M perpendicular to B): U = 0 → neutral, zero potential energy.
• At θ = 180° (M antiparallel to B): U_max = +mB → bar magnet is in the most unstable state with maximum potential energy.

A magnetic dipole placed in a uniform magnetic field experiences a torque given by τ = mB sin ⁡θ, or in vector form \[\vec τ\] = \[\vec M\] × \[\vec B\], where m is the magnetic dipole moment, B is the magnetic field, and θ is the angle between them. This torque tends to align the magnetic dipole moment vector with the magnetic field vector. It is responsible for various phenomena such as the behavior of compass needles aligning with Earth's magnetic field and the operation of electric motors based on the interaction between a magnetic field and current-carrying wires.

When a freely suspended magnetic dipole in a uniform magnetic field is slightly displaced from its equilibrium position, it performs angular oscillations with time period T = \[\frac {2π}{ω}\] = 2π\[\sqrt {\frac {I}{mB}}\], where I is the moment of inertia of the dipole, m is its magnetic dipole moment and B is the magnetic field strength.

When a ferromagnetic material is subjected to a cycle of magnetisation and demagnetisation, the intensity of magnetisation (I) or magnetic induction (B) lags behind the magnetising field (H). This lagging behaviour is called hysteresis. When plotted on a B–H graph, the curve forms a closed loop (hysteresis loop) in which:

• B₀​ (point A) denotes the saturation magnetic induction,
• The intercept OB (or OC) on the B-axis when H is reduced to zero represents retentivity (residual magnetism),
• The intercept OF on the H-axis (reverse field H_0​) needed to reduce B to zero represents coercivity,
• Points D and E represent reverse saturation and reverse retentivity respectively.

The area enclosed by the hysteresis loop is equal to the energy loss per cycle per unit volume of the material, and this area is different for different materials. Therefore, materials used as electromagnets require a narrow loop (low hysteresis loss), while permanent magnets require a wide loop (high retentivity and coercivity).

When a soft ferromagnetic material is kept in a uniform magnetic field, a large number of magnetic lines crowd up inside the material, leaving very few outside. For a closed structure, like an iron ring, kept in a magnetic field, very few lines of force pass through the enclosed space. This effect is known as magnetic shielding — a technique that uses materials with high magnetic permeability to redirect or absorb magnetic field lines, thereby reducing the magnetic field in a specific area.

The magnetization of a paramagnetic material is directly proportional to the applied magnetic field and inversely proportional to the absolute temperature is called Curie’s Law.

M = \[\frac {CB}{T}\]​

or

χ = \[\frac{C\mu_0}{T}\]​​

where
C = Curie constant
T = absolute temperature

Statement

Ferromagnetism is due to strong exchange interaction between neighbouring atomic magnetic moments, which causes them to align in small regions called domains.

Explanation

In ferromagnetic materials, atoms have permanent magnetic moments.
Due to strong exchange interaction, many neighbouring atomic dipoles align in the same direction, forming small regions called domains.

In an unmagnetized material, these domains are randomly oriented, so the net magnetic moment is zero.

When an external magnetic field is applied, domains aligned with the field grow in size. Under a strong magnetic field, all domains align in one direction, producing strong magnetisation.

Conclusion

Thus, ferromagnetism arises from the formation and alignment of magnetic domains driven by exchange interactions.

• Soft iron is used to make electromagnets because it has high permeability and low retentivity; it becomes magnetic when current flows and loses magnetism when the current is switched off.
• Permanent magnets are made from hard ferromagnetic materials that retain magnetisation even after the external magnetic field is removed.
• Soft magnetic materials are easily magnetised and demagnetised, while hard magnetic materials retain magnetisation for a longer time, as shown by their hysteresis loops.

• When the temperature increases, the exchange interaction weakens, and the domain structure gets disturbed; at Tc , the domains collapse completely.
• The temperature at which a ferromagnetic material changes into a paramagnetic state is called the Curie temperature, Tc.
• For T > T_c​, magnetic susceptibility is given by
  χ = \[\frac {C}{T-T_c}\]​