Magnetic Materials

Answer

τ = m⃗ × B⃗ = mB sin θ Where: - τ = torque - m = magnetic dipole moment - B = magnetic field intensity - θ = angle between m⃗ and B⃗ This torque causes the magnet to align with the magnetic field di…

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U = ∫₀^θ τ dθ = ∫₀^θ mB sin θ dθ U = -mB cos θ Special cases: - θ = 0°: U = -mB (minimum energy, stable) - θ = 90°: U = 0 - θ = 180°: U = +mB (maximum energy, unstable) The dipole tends to align wi…

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T = 2π√(I/mB) Where: - T = time period - I = moment of inertia of the magnet - m = magnetic dipole moment - B = magnetic field intensity This is derived from angular SHM equation: d²θ/dt² = -(mB/I)θ…

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For an electron in circular orbit: Current: I = ev/2πr Orbital magnetic moment: m_orb = IA = (ev/2πr) × πr² = ½evr Using L = m_e vr (angular momentum): m_orb = (e/2m_e)L For first orbit (n=1): m_or…

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Magnetization is the magnetic moment per unit volume of a material. M = m_net/Volume Units: A m⁻¹ Dimensions: [L⁻¹ A] Magnetization represents the extent to which a material is magnetized when plac…

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Magnetic susceptibility (χ) is a dimensionless quantity that indicates how easily a material can be magnetized. M = χH Where: - M = magnetization - H = magnetic field intensity - χ = magnetic suscep…

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B = μ₀(H + M) Where: - B = magnetic flux density - H = magnetic field intensity = nI - M = magnetization - μ₀ = permeability of free space Also: B = μH = μ_r μ₀ H μ = μ₀(1 + χ) where χ is magnetic s…

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Diamagnetic materials have all electrons paired, resulting in zero net magnetic moment. Properties: - χ < 0 (negative susceptibility) - Repelled by magnets - Move from stronger to weaker magnetic fie…