Magnetism and Matter

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A magnetic dipole moment (m) is the quantitative measure of the strength and orientation of a magnet. For a current loop: m = IA, where I is current (A) and A is area (m²). Units: A·m² (ampere meter s…

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Given: m = 0.5 A·m², B = 0.4 T, θ = 30° Formula: τ = mB sin θ Step 1: τ = 0.5 × 0.4 × sin(30°) Step 2: τ = 0.5 × 0.4 × 0.5 Step 3: τ = 0.1 N·m Answer: The torque is 0.1 N·m, directed to align the mome…

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Magnetic field lines form closed loops because magnetic monopoles (isolated magnetic poles) do not exist in nature. Every magnet has both north and south poles—they cannot be separated. Therefore, fie…

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Gauss's Law for Magnetism states: The net magnetic flux through any closed surface is zero. Mathematically: ∮ B·dS = 0 Physical Significance: This law confirms that isolated magnetic poles (monopoles)…

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Formula: U = -m·B = -mB cos θ Given: m = 0.8 A·m², B = 0.5 T, θ = 60° Step 1: U = -0.8 × 0.5 × cos(60°) Step 2: U = -0.8 × 0.5 × 0.5 Step 3: U = -0.2 J Answer: The potential energy is -0.2 J. Negative…

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For a bar magnet on its axis where r >> l: Formula: B_A = (μ₀/4π) × (2m/r³) Given: m = 1.2 A·m², r = 0.5 m, μ₀/4π = 10⁻⁷ T·m/A Step 1: B_A = 10⁻⁷ × (2 × 1.2)/(0.5)³ Step 2: B_A = 10⁻⁷ × 2.4/0.125 Step…

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Diamagnetic materials: Have χ < 0 (negative susceptibility), are weakly repelled by magnetic fields, have μ < μ₀. Electrons' magnetic moments pair up with zero net moment. Field lines are expelled. Ex…

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Magnetic intensity H is independent of core material: Formula: H = nI where n = number of turns per unit length, I = current Given: n = 500 turns/m, I = 2 A Step 1: H = 500 × 2 Step 2: H = 1000 A/m An…