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

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

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

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

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

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

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

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

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

The minimum temperature at which the domain structure of a ferromagnetic substance collapses completely and it is converted into a paramagnetic substance is called Curie temperature.

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 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.

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 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.

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): \[\vec τ\] = \[\vec M\] × \[\vec B\]

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.

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.

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.

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.

• Relative permeability ranges: μ_r < 1 (as B is less than μ₀H); also 1 > μ_r > 0, μ < μ₀
• Diamagnetic: B < B₀​; B_m < B₀
• Magnetic susceptibility (χ): low and negative, ∣χ∣ ≈ 1; small, negative and temperature-independent, χ_m ∝ T₀
• Magnetic moment: very low (≈ 0)
• Intensity of magnetisation (I) vs H: I is small, negative, varies linearly with H (I and H in opposite direction, I is negative with respect to H)

• Relative permeability ranges:  μ_r > 1 (as B is slightly greater than μ₀H); (1 + ε) ≥ μ_r > 1, μ > μ₀
• Diamagnetic: B < B₀​; B_m < B₀
• Magnetic susceptibility (χ): low and positive, χ ≈ 1; small, positive, varies inversely with temperature, χ_m ∝ \[\frac {1}{T}\]​ (Curie law)
• Magnetic moment: very low but not zero
• Intensity of magnetisation (I) vs H: I is small, positive, varies linearly with H (I and H in same direction, value of I is low)

• Relative permeability ranges:   μ_r ≫ 1, of the order of 10²; μ ≫ μ₀
• Diamagnetic: B ≫ B₀​; B_m ≫ B₀
• Magnetic susceptibility (χ): positive and high, χ ≈ 10²; very large, positive, temperature dependent, χ_m ∝ \[\frac {1}{T−T_C}\]​ (Curie–Weiss law)
• Magnetic moment: very high
• Intensity of magnetisation (I) vs H: I is very large, positive, varies non-linearly with H (I is in the direction of H, value of I is very high)