Electromagnetic Induction and Alternating Current

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Faraday's Law: The magnitude of the induced emf in a loop is equal to the rate of change of magnetic flux linked with it. For a single loop: |ε| = dΦ_B / dt For a coil with N turns: |ε_total| = N × …

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Lenz's Law: When a current is induced in a conductor, the direction of the induced current is such that its magnetic effect OPPOSES the change (in flux) that induced it. Combined Faraday-Lenz Law: ε …

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Given: N = 75 turns, R = 35 mm = 0.035 m B₁ = 25 mT = 0.025 T, B₂ = 50 mT = 0.050 T t = 250 ms = 0.250 s Rate of change of field: dB/dt = (B₂ − B₁)/t = (0.050 − 0.025)/0.250 = 0.10 T/s Flux per turn…

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Eddy Currents: When a solid conductor (like a metal sheet or plate) is placed in a changing magnetic field, induced closed loops of current are set up inside the bulk of the conductor. These are calle…

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Self-Inductance (L): It is the property of a coil by which it opposes any change in the current flowing through it. The magnetic flux linked with the coil is proportional to the current. Formula: Φ =…

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Step-by-Step Derivation: Step 1 – Magnetic field inside solenoid: Using Ampere's Law: B = μ₀ × n × I where n = N/ℓ (turns per unit length) Step 2 – Total magnetic flux through N turns: Φ = N × B × A…

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Given: ℓ = 1 m, diameter = 20 cm → radius = 0.10 m A = π × (0.10)² = π × 0.01 = 3.14 × 10⁻² m² N = 10,000 turns I₁ = 2.5 A, I₂ = 0 A, t = 1.0 ms = 1.0 × 10⁻³ s Step 1 – Find Self-Inductance: L = μ₀ N…

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Mutual Inductance (M): When two coils are placed close to each other, a changing current in coil A (primary) causes a changing flux through coil B (secondary), inducing an emf in B. This property is c…