Moving Charges and Magnetism

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The Lorentz Force is the total electromagnetic force experienced by a charged particle moving in the presence of both electric and magnetic fields. Mathematical Expression: F = q(E + v × B) Where: -…

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Given: - q = 1.6 × 10⁻¹⁹ C - v = 3 × 10⁷ m/s - B = 6 × 10⁻⁴ T - θ = 90° (perpendicular, so sin θ = 1) Formula: F = qvB sin θ Step 1: Substitute values F = (1.6 × 10⁻¹⁹) × (3 × 10⁷) × (6 × 10⁻⁴) × 1 …

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The magnetic force arises from the motion of charge through a magnetic field. The force is given by F = q(v × B). Key Physics Principle: 1. For stationary charges (v = 0): F = 0 because the velocity …

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Ampere's Circuital Law: The line integral of the magnetic field around any closed loop is equal to μ₀ times the current enclosed by that loop. Mathematical Form: ∮ B·dl = μ₀I_enclosed Simplified For…

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Given: - I = 10 A - r = 2 cm = 0.02 m - μ₀ = 4π × 10⁻⁷ T·m/A Formula (for infinite straight wire): B = (μ₀I)/(2πr) Step 1: Substitute values B = (4π × 10⁻⁷ × 10)/(2π × 0.02) Step 2: Cancel π terms …

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The fundamental difference stems from the nature of sources: Electric Field Lines: - Originate from positive charges (sources) - Terminate at negative charges (sinks) - Because electric monopoles (is…

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Biot-Savart Law: The magnetic field dB produced by a small current element at a distance r is: dB = (μ₀/4π) × (I dl sin θ)/r² Vector Form: dB = (μ₀/4π) × (I dl × r)/r³ Where: - dB = Magnetic field …

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For Semicircular Wire: Given: - R = 5 cm = 0.05 m - I = 10 A - μ₀ = 4π × 10⁻⁷ T·m/A Step 1: For semicircle, use formula (half of complete loop) B_semi = (1/2) × (μ₀I)/(2R) B_semi = (μ₀I)/(4R) Step …