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Faraday's laws form the quantitative foundation of electromagnetic induction. The first law states that a changing magnetic flux through a circuit induces an EMF. The second law quantifies it: $\varepsilon = -Nd\Phi_B/dt$, where $N$ is the number of turns and $\Phi_B = \int\vec{B}\cdot d\vec{A}$.

Three mechanisms change flux: (1) Time-varying $B$ (e.g., a coil near an electromagnet being switched on/off). (2) Changing area (e.g., a rod sliding on rails, expanding/contracting loop). (3) Changing angle (e.g., a coil rotating in a uniform field — the AC generator). Any combination also works.

Critical distinctions: flux ($\Phi$) is a state quantity — it can be large with zero EMF (when constant). EMF depends on the rate of change ($d\Phi/dt$), not the flux itself. Maximum EMF occurs when flux is changing fastest (passing through zero in sinusoidal cases), not when flux is maximum.

The total charge flowed is $Q = N\Delta\Phi/R$, independent of the rate of change. A fast change gives large current briefly; a slow change gives small current for longer. This property is used in search coils and ballistic galvanometers for magnetic field measurement.