Electromagnetic Induction

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Electromagnetic induction is the phenomenon in which an EMF (and current) is induced in a conductor when the magnetic flux through it changes. The basic principle: A changing magnetic field produces a…

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Magnetic flux (φB) is the measure of magnetic field lines passing through a given area. Mathematically: φB = B⃗ · A⃗ = BA cos θ, where B is magnetic field, A is area of the surface, and θ is angle bet…

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Faraday's Law states that the magnitude of induced EMF in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically: |ε| = |dφB/dt|. For a co…

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Lenz's Law: The direction of induced current is such that it opposes the change causing it. Physical significance: It's a consequence of conservation of energy. If induced current aided the change, we…

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Given: N = 100 turns, r = 5 cm = 0.05 m, B₁ = 0.1 T, B₂ = 0.5 T, t = 0.2 s Solution: Area A = πr² = π(0.05)² = π × 0.0025 = 7.85 × 10⁻³ m² Change in flux: Δφ = A(B₂ - B₁) = 7.85 × 10⁻³ × (0.5 - 0.1) =…

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Motional EMF is the EMF induced in a conductor moving through a magnetic field. Derivation: Consider a rod of length l moving with velocity v perpendicular to magnetic field B. In time t, rod moves di…

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Given: l = 50 cm = 0.5 m, v = 10 m/s, B = 0.8 T For motional EMF: ε = Blv ε = 0.8 × 0.5 × 10 = 4.0 V The motional EMF induced across the ends of the rod is 4.0 V.

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Eddy currents are circular currents induced in bulk conductors when exposed to changing magnetic fields, named after Foucault (1895). Applications: (1) Electromagnetic brakes in trains (2) Induction f…