Electromagnetic Induction

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Whenever there is a change of magnetic flux in a closed circuit, an induced EMF is produced in the circuit. Also, if a conductor cuts the lines of magnetic field, an EMF is induced between its ends. T…

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e = -dφ/dt, where e is induced EMF, φ is magnetic flux, and t is time. The negative sign incorporates Lenz's law. For a coil of N turns: e = -N(dφ'/dt). This quantitative law gives the magnitude of in…

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Lenz's Law: The direction of induced current is such that the magnetic field produced by it opposes the change in magnetic flux that induces the current. This follows from energy conservation - if ind…

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Magnetic flux through a surface is the measure of magnetic field lines passing through that surface. For a small area: dφ = B⃗ · da⃗ = B da cos θ. For finite area: φ = ∫ B⃗ · da⃗. Unit: Weber (Wb). It…

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Given: l = 0.5 m, v = 10 m/s, B = 0.2 T, θ = 90° Formula: e = Blv sin θ Solution: e = 0.2 × 0.5 × 10 × sin 90° e = 0.2 × 0.5 × 10 × 1 = 1.0 V The induced EMF is 1.0 V.

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For a rod of length l rotating with angular velocity ω in perpendicular magnetic field B: Consider element dr at distance r: de = Bv dr = Bωr dr Total EMF: e = ∫₀ˡ Bωr dr = Bω ∫₀ˡ r dr = Bω[r²/2]₀ˡ Th…

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Self-inductance (L) is the property of a coil by which it opposes changes in current through itself. Definition: L = φ/i (flux per unit current) or L = |e|/(di/dt) (EMF per unit rate of change of curr…

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For a solenoid: B = μ₀ni (inside), where n = N/l Flux per turn: φ' = BA = μ₀niA Total flux linkage: Nφ' = N × μ₀(N/l)iA = μ₀N²iA/l Self-inductance: L = Nφ'/i = μ₀N²A/l For unit length: L/l = μ₀n²A = μ…