Magnetism and Matter

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1. Earth behaves as a magnet with magnetic field pointing from geographic south to north 2. A freely suspended bar magnet points in north-south direction 3. Like poles repel, unlike poles attract 4. M

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1. Magnetic field lines form continuous closed loops (unlike electric field lines) 2. Tangent to field line at any point gives direction of magnetic field B at that point 3. Greater density of field l

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A bar magnet can be thought of as equivalent to a solenoid because: 1. Both produce similar magnetic field line patterns 2. Cutting a bar magnet is like cutting a solenoid - creates two smaller units

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For a magnetic dipole with moment m in uniform field B: Torque τ = m × B Magnitude: τ = mB sin θ where θ is angle between m and B This is a restoring torque that tends to align the dipole with the fi

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Potential energy: U = -m⃗ · B⃗ = -mB cos θ Key points: • Minimum energy (most stable): θ = 0° (U = -mB) • Maximum energy (least stable): θ = 180° (U = +mB) • Zero potential energy reference: θ = 90°

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For a bar magnet with moment m at distance r >> l: Axial field: B_A = (μ₀/4π) × (2m/r³) Equatorial field: B_E = (μ₀/4π) × (m/r³) Note: Axial field is twice the equatorial field at same distance. Bot

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Gauss's Law for Magnetism: The net magnetic flux through any closed surface is zero. Mathematically: ∮ B⃗ · dS⃗ = 0 Physical significance: • No isolated magnetic poles (monopoles) exist • Magnetic f

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Magnetization (M): Net magnetic moment per unit volume of a material. Formula: M = m_net/V Where: • m_net = net magnetic moment of the sample • V = volume of the sample Units: A/m (ampere per meter