Overview: Magnetic Materials

τ = m × B

Magnitude:

τ = m B sin θ

U = −m B cos θ

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

m_orb​ = IA

For an electron revolving in a circular orbit:

m_orb​ = \[\frac {evr}{2}\]

It is the ratio of magnetic moment to angular momentum.

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

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

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

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

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

M = _χH

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

μ_r = 1 + χ

B = μ₀​(1 + χ)H

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

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 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.

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

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

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.

• 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 = \[\frac {C}{T-T_c}\]​

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

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

• 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.

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.