#ferromagnetism

Magnetic Field Due to Bar Magnet - Axial and Equatorial

In a material where magnetic domains spontaneously align over large regions, the susceptibility is:

**Magnetic field of bar magnet** follows inverse cube law B ∝ m/r³, unlike inverse square for electric dipole. Given B at distance r, moment m = B r³/(μ₀/4π) for equatorial, m = B r³/(2·μ₀/4π) for axial, enabling moment extraction from measured field. Ferromagnetic materials have magnetic domains that spontaneously align, resulting in a large positive susceptibility ( chi gg 1 ). This strong magnetization occurs due to cooperative interactions among atomic magnetic moments, distinguishing them from other materials. Substituting values gives Large and positive, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Magnetic Field Due to Bar Magnet - Axial and Equatorial

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Diamagnetism, Paramagnetism and Ferromagnetism

Which material has a large positive \( \chi \) and exhibits spontaneous domain alignment?

**Paramagnetism** has small positive χ ≈ 10⁻³ to 10⁻⁵, weakly attracted towards stronger field, random moments align partially with B, magnetization decreases with temperature following Curie law χ ∝ 1/T. Materials have unpaired electrons with permanent moments. Ferromagnetic materials have a large positive chi and exhibit spontaneous alignment of magnetic moments into domains. Substituting values gives Ferromagnetic, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Diamagnetism, Paramagnetism and Ferromagnetism

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Magnetic Field Lines, Bar Magnet and Dipole Moment

Which material has a large positive \( \chi \) and forms domains?

**Bar magnet properties** include dipole moment m = pole strength × separation, unit A·m², field lines emerge from north and enter south outside. Lines never cross, ensuring single valued B at any point, and pattern reflects dipole nature with symmetric loops around magnet. Ferromagnetic materials have large positive chi and exhibit domain formation due to spontaneous alignment of magnetic moments. Substituting values gives Ferromagnetic, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Magnetic Field Lines, Bar Magnet and Dipole Moment

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Diamagnetism, Paramagnetism and Ferromagnetism

A material’s susceptibility becomes large and positive when its microscopic regions align spontaneously. This is a featu

**Diamagnetism** exhibits small negative susceptibility χ ≈ -10⁻⁵ to -10⁻⁶, weakly repelled from stronger to weaker field regions, no permanent moment, induced moment opposite to B, present in all materials but dominated by other effects. Superconductor perfect diamagnet with χ = -1, complete field expulsion. Ferromagnetic materials exhibit large, positive susceptibility due to the spontaneous alignment of magnetic domains, which amplifies the magnetization far beyond that of paramagnetic or diamagnetic materials. Substituting values gives Ferromagnetic materials, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Diamagnetism, Paramagnetism and Ferromagnetism

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Magnetization, Magnetic Intensity, Susceptibility and Permeability

A material that exhibits strong magnetism due to the growth and alignment of microscopic domains when placed in an exter

**Magnetization M** is magnetic moment per unit volume (A/m), magnetic intensity H = B/μ₀ - M, susceptibility χ = M/H dimensionless, permeability μ = B/H = μ₀(1+χ), relative permeability μ_r = μ/μ₀ = 1+χ. For solenoid with core, B = μ₀ μ_r n I, n turns per meter (m⁻¹), I current (A). Ferromagnetic materials have microscopic domains that align and grow in the presence of an external magnetic field, leading to strong magnetization. This cooperative behavior amplifies the field inside the material significantly. Substituting values gives Ferromagnetic, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Magnetization, Magnetic Intensity, Susceptibility and Permeability

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