Magnetism and Magnetic Effect of Electric Current

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Biot-Savart's Law: The magnetic field dB due to a small current element (I·dℓ) at a point P at distance r is: |dB| = (μ₀/4π) × (I·dℓ·sinθ) / r² Where: • μ₀ = Permeability of free space = 4π × 10⁻⁷ T…

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Given: • r = 5 cm = 0.05 m • I = 2 A • n = 1 turn Formula: |B| = μ₀I / 2r Step 1: Substitute values B = (4π × 10⁻⁷ × 2) / (2 × 0.05) Step 2: Calculate numerator 4π × 10⁻⁷ × 2 = 8π × 10⁻⁷ Step 3: C…

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Given: • n = 500 turns/m • I = 3 A Formula (inside solenoid): B = μ₀nI Step 1: Substitute values B = 4π × 10⁻⁷ × 500 × 3 Step 2: Calculate B = 4π × 10⁻⁷ × 1500 B = 6000π × 10⁻⁷ B = 6π × 10⁻⁴ T Ste…

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Ampere's Circuital Law: The line integral of magnetic field B around any closed loop equals μ₀ times the total current I passing through the loop. Mathematical Form: ∮ B·dl = μ₀I Key Points: • The c…

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Given: • I = 12 A • B = 3 × 10⁻⁵ T Formula (infinite straight wire): B = μ₀I / 2πr Rearranging for r: r = μ₀I / 2πB Step 1: Note that μ₀/2π = 2 × 10⁻⁷ T·m·A⁻¹ Step 2: Substitute values r = (2 × 10…

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Lorentz Force: The force experienced by a charged particle moving in a magnetic field is called the Lorentz force. Formula: F = q(v × B) |F| = qvB sinθ Where: • q = charge of particle (Coulombs) • v…

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Given: • v = 3 × 10⁷ m/s • B = 0.2 T • mₑ = 9 × 10⁻³¹ kg • e = 1.6 × 10⁻¹⁹ C • θ = 90° (perpendicular) Formula: R = mv / qB (Magnetic force provides centripetal force: qvB = mv²/R) Step 1: Substitut…

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Derivation: For circular motion in magnetic field: Magnetic force = Centripetal force qvB = mv²/R ∴ R = mv/qB ...(1) Time period T = Circumference / Speed T = 2πR/v Substitute R from (1): T = 2π(mv…