CBSE Class 12 Board Examination

Chapter 6: Electromagnetic Induction

Summary

A changing magnetic flux through a circuit induces an emf—the heart of electromagnetic induction. Magnetic flux is \(\Phi=\vec{B}\cdot\vec{A}=BA\cos\theta\). Faraday's law states that the induced emf equals the rate of change of flux, \(\varepsilon=-\dfrac{d\Phi}{dt}\), while Lenz's law, expressed by the negative sign, ensures the induced current opposes the change producing it—a statement of energy conservation. A conductor of length \(l\) moving with speed \(v\) across a field generates a motional emf \(\varepsilon=Blv\). Changing fluxes also drive eddy currents in bulk conductors, used in braking and induction heating but minimised by lamination in transformers. Self-inductance \(L\) opposes changes in a coil's own current, with emf \(\varepsilon=-L\dfrac{dI}{dt}\) and stored energy \(U=\tfrac{1}{2}LI^2\). Mutual inductance \(M\) couples two coils, the basis of the transformer. An AC generator converts mechanical energy into electrical energy by rotating a coil in a field, producing a sinusoidal emf \(\varepsilon=\varepsilon_0\sin\omega t\), embodying the link between motion, magnetism and electricity.

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