#magnetic susceptibility

Earth's Magnetism and Magnetic Declination

A paramagnetic material with \( \chi = 3 \times 10^{-3} \) in \( H = 400 \, \text{A m}^{-1} \) has magnetization \( M \)

**Geomagnetic field** arises from outer core dynamo, field lines emerge near geographic south pole. Understanding D and I allows conversion between geographic and magnetic coordinates, with B_H = B cos(inclination) used in experiments with tangent galvanometer. M = chi H . Given: chi = 3 × 10⁻³ , H = 400 A m⁻¹ . M = 3 × 10⁻³ × 400 = 1.2 A m⁻¹ . Substituting values gives 1.2 A m⁻¹, 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 > Earth's Magnetism and Magnetic Declination

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Earth's Magnetism and Magnetic Declination

A material’s susceptibility becomes negative and large when:

**Elements of Earth's field** include declination D, inclination I, horizontal component B_H, total field B = √(B_H² + B_V²). B_H provides compass direction, declination varies with location, important for navigation, inclination 0° at magnetic equator, 90° at poles. A superconductor has a susceptibility of chi = -1 (large and negative) when it transitions to the superconducting state below its critical temperature, expelling all magnetic fields via the Meissner effect, a unique property among materials. Substituting values gives It becomes superconducting, which matches expected magnitude for

Ref: NCERT > Physics Book > Magnetism and Matter > Earth's Magnetism and Magnetic Declination

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Earth's Magnetism and Magnetic Declination

A material with susceptibility \( \chi = 5 \times 10^{-3} \) has a relative permeability \( \mu_r \) of:

**Geomagnetic field** arises from outer core dynamo, field lines emerge near geographic south pole. Understanding D and I allows conversion between geographic and magnetic coordinates, with B_H = B cos(inclination) used in experiments with tangent galvanometer. μ_r = 1 + chi . Given: chi = 5 × 10⁻³ . Substitute: μ_r = 1 + 5 × 10⁻³ = 1.005 . Substituting values gives 1.005, 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 > Earth's Magnetism and Magnetic Declination

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Earth's Magnetism and Magnetic Declination

A paramagnetic material with \( \chi = 4 \times 10^{-4} \) in \( H = 2000 \, \text{A m}^{-1} \) has magnetization \( M \

**Geomagnetic field** arises from outer core dynamo, field lines emerge near geographic south pole. Understanding D and I allows conversion between geographic and magnetic coordinates, with B_H = B cos(inclination) used in experiments with tangent galvanometer. M = chi H . Given: chi = 4 × 10⁻⁴ , H = 2000 A m⁻¹ . M = 4 × 10⁻⁴ × 2000 = 0.8 A m⁻¹ . Substituting values gives 0.8 A m⁻¹, 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 > Earth's Magnetism and Magnetic Declination

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Earth's Magnetism and Magnetic Declination

Which material has \( \chi = -1 \) and completely expels magnetic field lines?

**Elements of Earth's field** include declination D, inclination I, horizontal component B_H, total field B = √(B_H² + B_V²). B_H provides compass direction, declination varies with location, important for navigation, inclination 0° at magnetic equator, 90° at poles. Superconductors have chi = -1 and exhibit perfect diamagnetism, expelling all magnetic field lines (Meissner effect). Substituting values gives Superconductor, 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 > Earth's Magnetism and Magnetic Declination

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A paramagnetic material with \( \chi = 8 \times 10^{-4} \) in \( H = 2500 \, \text{A m}^{-1} \) has magnetization \( M \

**Hysteresis loop** plots B versus H for ferromagnetic material, retentivity (remanence) is residual B at H=0 after saturation, coercivity is reverse H needed to reduce B to zero. Hard ferromagnets have high retentivity and coercivity, retaining strong magnetism after external field removed, suitable for permanent magnets. M = chi H . Given: chi = 8 × 10⁻⁴ , H = 2500 A m⁻¹ . M = 8 × 10⁻⁴ × 2500 = 2 A m⁻¹ . Substituting values gives 2.0 A m⁻¹, 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 > Hysteresis, Retentivity, Coercivity and Permanent Magnets

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A diamagnetic material has a susceptibility \( \chi = -2 \times 10^{-5} \). What is its magnetic permeability \( \mu \)

**Permanent magnet requirement** is high retentivity to maintain field and high coercivity to resist demagnetization. Ability to retain magnetism after field removal is property of hard ferromagnets, related to domain wall pinning and anisotropy. Magnetic permeability μ = μ₀ (1 + chi) . Given: chi = -2 × 10⁻⁵ . Substitute: μ = μ₀ (1 - 2 × 10⁻⁵) = μ₀ × 0.99998 . Substituting values gives μ₀ × 0.99998, 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 > Hysteresis, Retentivity, Coercivity and Permanent Magnets

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Diamagnetism, Paramagnetism and Ferromagnetism

A paramagnetic material has \( \chi = 5 \times 10^{-4} \) and \( H = 2 \times 10^3 \, \text{A m}^{-1} \). What is its ma

**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. M = chi H . Given: chi = 5 × 10⁻⁴ , H = 2 × 10³ A m⁻¹ . Substitute: M = 5 × 10⁻⁴ × 2 × 10³ = 1 A m⁻¹ . Substituting values gives 1 A m⁻¹, 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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Diamagnetism, Paramagnetism and Ferromagnetism

A material with susceptibility \( \chi = -5 \times 10^{-5} \) has a relative permeability \( \mu_r \) of:

**Ferromagnetism** shows large positive χ ≈ 10³ to 10⁵, strong attraction, domain structure with spontaneous magnetization, hysteresis, retentivity. Distinction based on sign and magnitude of χ and behaviour in non-uniform field, explaining attraction versus repulsion. μ_r = 1 + chi . Given: chi = -5 × 10⁻⁵ . Substitute: μ_r = 1 - 5 × 10⁻⁵ = 0.99995 . Substituting values gives 0.99995, 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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Diamagnetism, Paramagnetism and Ferromagnetism

A material’s magnetic susceptibility becomes zero when:

**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. For a superconductor below its critical temperature, the susceptibility chi = -1 and relative permeability μ_r = 0 , but in a broader context, susceptibility can approach zero for non-magnetic materials or when magnetization is negligible compared to the applied field. However, the question implies a specific state, and superconductors

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

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Diamagnetism, Paramagnetism and Ferromagnetism

A paramagnetic material with \( \chi = 9 \times 10^{-4} \) in \( H = 2000 \, \text{A m}^{-1} \) has magnetization \( M \

**Ferromagnetism** shows large positive χ ≈ 10³ to 10⁵, strong attraction, domain structure with spontaneous magnetization, hysteresis, retentivity. Distinction based on sign and magnitude of χ and behaviour in non-uniform field, explaining attraction versus repulsion. M = chi H . Given: chi = 9 × 10⁻⁴ , H = 2000 A m⁻¹ . M = 9 × 10⁻⁴ × 2000 = 1.8 A m⁻¹ . Substituting values gives 1.8 A m⁻¹, 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 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

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

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