0Definition:
Electromagnetic induction is the phenomenon in which a changing magnetic field induces an electromotive force (EMF) in a conductor.
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Discovered by Michael Faraday in 1831.
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Later formulated mathematically by Joseph Henry (independently).
📌 Faraday’s Law of Electromagnetic Induction
The induced EMF in a circuit is proportional to the rate of change of magnetic flux through the circuit.
E=−dΦBdt\mathcal{E} = - \frac{d\Phi_B}{dt}E=−dtdΦB
Where:
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E\mathcal{E}E = induced EMF (V)
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ΦB=B⋅A⋅cosθ\Phi_B = B \cdot A \cdot \cos\thetaΦB=B⋅A⋅cosθ = magnetic flux (Wb)
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BBB = magnetic field, AAA = area, θ\thetaθ = angle between B and normal to the loop
Negative sign → Lenz’s Law (opposition to change in flux).
📌 Lenz’s Law
The direction of induced current (or EMF) opposes the change in magnetic flux that produced it.
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This is a consequence of conservation of energy.
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Example: If flux increases → induced current creates opposite field to resist increase.
🔹 Motional EMF
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When a conductor of length lll moves with velocity vvv perpendicular to magnetic field BBB:
