Revision: 12th Std >> Magnetic Materials MAH-MHT CET (PCM/PCB) Magnetic Materials

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

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

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 a vacuum and induces magnetism is called a 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 the magnetising field to the permeability of free space is called magnetic intensity.

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

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

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

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 the 'intensity of magnetisation'.

Substances which when placed in a magnetic field are feebly magnetised in a direction opposite to that of the magnetising field are called diamagnetic substances.

Substances which when placed in a magnetic field are feebly magnetised in the direction of the magnetising field are called paramagnetic substances.

Substances which when placed in a magnetising field are strongly magnetised in the direction of the magnetising field are called ferromagnetic substances.

The point beyond which M does not increase further with increasing H, as all domains are aligned.

The phenomenon in which magnetisation M (or flux density B) lags behind the magnetising field H during a cycle of magnetisation.

Residual magnetisation retained by the material when H is reduced to zero after saturation.

SI Unit: A/m

The reverse magnetising field required to reduce residual magnetisation to zero.

SI Unit: A/m

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

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

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

B = μ₀​(H + M)

• SI unit: tesla (T)

M = χH

or

χ = HM​

B = μH

• SI unit: H/m

μr ​= \[\frac {μ}{​μ_0}\]

M = \[\frac {\text {magnetic moment​}}{\text {volume}}\]

• SI unit: A/m

H = nI

where n is the number of turns per unit length and I is current.

• SI unit: A/m

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.

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.

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.

For ferromagnetic substances above the Curie temperature, the magnetic susceptibility is inversely proportional to (T − T_C), where T_C is the Curie temperature. Mathematically,

On heating beyond the Curie temperature (T_C(iron) = 770 °C), ferromagnetic substances get converted into paramagnetic materials.

The magnetic susceptibility of a paramagnetic material varies inversely with its absolute temperature. Mathematically,

On cooling, paramagnetic substances get converted to ferromagnetic materials at the Curie temperature.

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.

• Diamagnetic substances are weakly repelled and have negative susceptibility.
• Paramagnetic substances are weakly attracted and obey Curie law.
• Ferromagnetic substances are strongly attracted and contain domains.
• Ferromagnets become paramagnetic above the Curie temperature.
• The comparison table is the most important revision tool for board preparation.