Magnetism

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Magnetism is the property of any object by virtue of which it can attract pieces of iron, cobalt, or nickel. Five basic properties: 1. Directive Property - freely suspended magnet aligns north-south

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Magnetic field (B⃗) is a vector quantity representing the region around a magnet where a magnetic needle experiences torque and rests in a definite direction. Magnetic field lines: - Imaginary lines

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For a bar magnet of length l, pole strength m, in uniform field B at angle θ: Forces: +mB on N-pole, -mB on S-pole Normal distance between forces = l sin θ Torque τ = Force × Normal distance τ = mB

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Magnetic Flux (φB): The magnetic field lines passing through a surface area in a magnetic field. φB = B⃗ · A⃗ = BA cos θ where θ is angle between B⃗ and area vector A⃗ SI unit: Weber (Wb) Magnetic Fi

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Gauss's Law in Magnetism: The net magnetic flux through any closed surface is zero. Mathematically: φB = Σ B⃗ · ΔA⃗ = 0 Explanation: Magnetic field lines form closed loops, so equal number of lines

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Starting from torque: τ = MB sin θ Potential energy is work done against torque: Um = ∫ τ dθ = ∫ MB sin θ dθ Um = -MB cos θ + C Taking Um = 0 at θ = 90°: Um = -MB cos θ Minimum energy: Um = -MB at

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Magnetization (I): Magnetic moment per unit volume I = M/V = m/A (pole strength per unit cross-sectional area) Unit: A/m Magnetic Intensity (H): External magnetic field influence, independent of mate

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Magnetic Permeability (μ): Ability of material to permit passage of magnetic field lines μ = B/H Magnetic Susceptibility (χ): Ratio of magnetization to magnetizing force χ = I/H Relationship derivat