Magnetism and magnetic effects of electric current

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Magnetic dipole moment (p_m) is defined as the product of pole strength (q_m) and magnetic length (2l). Formula: p_m = q_m × 2l. SI unit: A·m² (ampere-meter squared) or J·T⁻¹ (joule per tesla). Direct…

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For a short bar magnet on the axial line: B_axial = (μ₀/4π) × (2p_m/r³). Given: p_m = 2.5 A·m², r = 0.2 m, μ₀/4π = 10⁻⁷ T·m/A. Step 1: B = 10⁻⁷ × (2 × 2.5)/(0.2)³. Step 2: B = 10⁻⁷ × 5/0.008. Step 3: …

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A compass needle is a small magnet with its own magnetic dipole moment. The Earth itself behaves like a giant bar magnet with magnetic poles near the geographic poles. When freely suspended, the compa…

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The angle of dip (inclination) I is given by: tan(I) = B_V/B_H. Given: B_H = 0.18 G, B_V = 0.32 G. Step 1: tan(I) = 0.32/0.18 = 1.778. Step 2: I = tan⁻¹(1.778) = 60.5°. Step 3: Verify with resultant B…

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Coulomb's Law of Magnetism: F = k(q_m1 × q_m2)/r², where q_m is pole strength in A·m, k = μ₀/4π = 10⁻⁷ T·m/A. Like poles repel, unlike poles attract. Comparison with Electrostatics: Both follow invers…

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Using Coulomb's law of magnetism: F = (μ₀/4π) × (q_m1 × q_m2)/r². Given: q_m1 = q_m2 = 40 A·m, r = 10 cm = 0.1 m, μ₀/4π = 10⁻⁷ T·m/A. Step 1: F = 10⁻⁷ × (40 × 40)/(0.1)². Step 2: F = 10⁻⁷ × 1600/0.01.

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On the equatorial line (perpendicular bisector of a bar magnet), the magnetic field is: B_equatorial = -(μ₀/4π) × (p_m/r³). The negative sign indicates the field points opposite to the magnetic moment…

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Torque on a dipole in magnetic field: τ = p_m × B × sin(θ). Given: p_m = 0.5 A·m², B = 0.35 × 10⁻⁴ T, θ = 30°. Step 1: τ = 0.5 × 0.35 × 10⁻⁴ × sin(30°). Step 2: sin(30°) = 0.5. Step 3: τ = 0.5 × 0.35 …