Hysteresis, Retentivity, Coercivity and Permanent Magnets

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.

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A bar magnet with magnetic moment \( 0.8 \, \text{A m}^2 \) is placed at a distance of \( 0.4 \, \text{m} \) along its a

**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. The magnetic field along the axis is B = (μ₀/4π) (2m/r³) . Given: m = 0.8 A m² , r = 0.4 m , (μ₀/4π) = 10⁻⁷ . Substitute: B = 10⁻⁷ × (2 × 0.8/(0.4)³) = 10⁻⁷ × (1.6/0.064) = 2.5 × 10⁻⁶ T . Substituting values gives 2.5 × 10⁻⁶ T, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

The magnetic potential energy of a dipole with moment \( 0.4 \, \text{A m}^2 \) in a uniform magnetic field of \( 0.5 \,

**Soft ferromagnetic materials** have low coercivity and retentivity, narrow hysteresis loop, lose magnetism when external field removed, ideal for electromagnets and transformer cores. Energy loss per cycle proportional to loop area, explaining why soft materials minimize loss. Magnetic potential energy is U_m = -m B cosθ . Given: m = 0.4 A m² , B = 0.5 T , θ = 30° , cos 30° = (√(3)/2) ≈ 0.866 . Substitute: U_m = -0.4 × 0.5 × 0.866 = -0.1732 J ≈ -0.17 J . Substituting values gives -0.17 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

The magnetic field contribution \( B_m \) due to a material with \( M = 1.6 \times 10^5 \, \text{A m}^{-1} \) is: (Take

**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. B_m = μ₀ M . Given: M = 1.6 × 10⁵ A m⁻¹ , μ₀ = 4π × 10⁻⁷ . B_m = 4π × 10⁻⁷ × 1.6 × 10⁵ = 0.20096 T ≈ 0.20 T . Substituting values gives 0.20 T, 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 dipole with \( m = 0.8 \, \text{A m}^2 \) in a field \( B = 0.3 \, \text{T} \) at \( 90^\circ \) has potential energy:

**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. U_m = -m B cosθ . Given: m = 0.8 A m² , B = 0.3 T , θ = 90° , cos 90° = 0 . U_m = -0.8 × 0.3 × 0 = 0 J . Substituting values gives 0 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A bar magnet with magnetic moment \( 0.9 \, \text{A m}^2 \) is placed at a distance of \( 0.3 \, \text{m} \) along its a

**Soft ferromagnetic materials** have low coercivity and retentivity, narrow hysteresis loop, lose magnetism when external field removed, ideal for electromagnets and transformer cores. Energy loss per cycle proportional to loop area, explaining why soft materials minimize loss. The magnetic field along the axis is B = (μ₀/4π) (2m/r³) . Given: m = 0.9 A m² , r = 0.3 m , (μ₀/4π) = 10⁻⁷ . Substitute: B = 10⁻⁷ × (2 × 0.9/(0.3)³) = 10⁻⁷ × (1.8/0.027) ≈ 6.67 × 10⁻⁶ T . Substituting values gives 6.67 × 10⁻⁶ T, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A bar magnet with \( m = 0.75 \, \text{A m}^2 \) produces a field at \( 0.15 \, \text{m} \) on its equatorial line. What

**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. B = (μ₀/4π) (m/r³) . Given: m = 0.75 A m² , r = 0.15 m , (μ₀/4π) = 10⁻⁷ . B = 10⁻⁷ × (0.75/(0.15)³) = 10⁻⁷ × (0.75/0.003375) ≈ 2.222 × 10⁻⁵ T ≈ 2.22 × 10⁻⁵ T . Substituting values gives 2.22 × 10⁻⁵ T, which matches expected magnitude for this magnetic configuration, confirming dipole field

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A material with \( \mu_r = 800 \) and \( H = 250 \, \text{A m}^{-1} \) has \( B \): (Take \( \mu_0 = 4\pi \times 10^{-7}

**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. B = μ₀ μ_r H . Given: μ_r = 800 , H = 250 A m⁻¹ , μ₀ = 4π × 10⁻⁷ . B = 4π × 10⁻⁷ × 800 × 250 = 0.2512 T ≈ 0.25 T . Substituting values gives 0.25 T, 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

The torque on a magnetic dipole in a uniform magnetic field is zero when:

**Soft ferromagnetic materials** have low coercivity and retentivity, narrow hysteresis loop, lose magnetism when external field removed, ideal for electromagnets and transformer cores. Energy loss per cycle proportional to loop area, explaining why soft materials minimize loss. The torque on a magnetic dipole is given by tau = m B sinθ . It becomes zero when sinθ = 0 , which occurs when the dipole is aligned with the field ( θ = 0° ) or anti-aligned ( θ = 180° ), as the cross product m × B vanishes. Substituting values gives The dipole is parallel or anti-parallel to the field, which matches expected

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

A material with \( B = 0.48 \, \text{T} \) and \( H = 3200 \, \text{A m}^{-1} \) has \( M \): (Take \( \mu_0 = 4\pi \tim

**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. B = μ₀ (H + M) , so M = (B/μ₀) - H . Given: B = 0.48 T , H = 3200 A m⁻¹ , μ₀ = 4π × 10⁻⁷ . (B/μ₀) = (0.48/4π × 10⁻⁷) ≈ 3.819 × 10⁵ A m⁻¹ . M = 3.819 × 10⁵ - 3200 ≈ 3.787 × 10⁵ A m⁻¹ . Substituting

Ref: NCERT > Physics Book > Magnetism and Matter > Hysteresis, Retentivity, Coercivity and Permanent Magnets

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Hysteresis, Retentivity, Coercivity and Permanent Magnets

The strongest magnetic field of a bar magnet is observed:

**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. The magnetic field of a bar magnet is strongest at its poles, where field lines are most concentrated, as opposed to the central region where the field is weaker and less dense. Substituting values gives At its poles, 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

The magnetic field inside a bar magnet is directed from:

**Soft ferromagnetic materials** have low coercivity and retentivity, narrow hysteresis loop, lose magnetism when external field removed, ideal for electromagnets and transformer cores. Energy loss per cycle proportional to loop area, explaining why soft materials minimize loss. Inside a bar magnet, magnetic field lines run from the south pole to the north pole to form closed loops with the external field (north to south), maintaining continuity as there are no magnetic monopoles. Substituting values gives South to north, 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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