Electromagnetic Induction

If moving charges create magnetic fields (Chapters 4-5), can changing magnetic fields create currents? Faraday and Henry's famous experiments around 1830 answered with a resounding yes — and this chapter, a guaranteed scorer worth 4-7 Board marks and 1-2 JEE/NEET questions every year, builds the whole story. We start with the three classic coil-and-magnet experiments, define magnetic flux $\Phi_B = \vec{B}\cdot\vec{A} = BA\cos\theta$, and arrive at Faraday's law $\varepsilon = -N\frac{d\Phi_B}{dt}$. Lenz's law fixes the polarity of the induced emf — the induced current always opposes the change that produced it — and we see why this is nothing but conservation of energy. Moving a rod through a field gives the motional emf $\varepsilon = Blv$ (and $\frac{1}{2}B\omega R^2$ for a rotating rod), explained beautifully by the Lorentz force. We then quantify how circuits talk to each other through mutual inductance ($M_{12} = M_{21} = \mu_0 n_1 n_2 \pi r_1^2 l$ for coaxial solenoids) and how a coil resists changes in its own current through self-inductance ($L = \mu_0 n^2 Al$, the electromagnetic analogue of mass), storing magnetic energy $\frac{1}{2}LI^2$ with density $B^2/2\mu_0$. The chapter closes with the crown jewel of applications: the AC generator, $\varepsilon = NBA\omega\sin\omega t$, the machine on which modern civilisation runs. Every derivation, every standard numerical and every exam-favourite reasoning question is covered.