Q.A circular coil of 100 turns with a cross-sectional area (A) of 1 m$^2$ is kept with its plane perpendicular to the magnetic field (B) of 1 T. What is the magnetic flux linkage with the coil? (A) 1 Wb (B) 100 Wb (C) 50 Wb (D) 200 Wb

Faraday's Law of electromagnetic induction has two parts. The First Law (qualitative) states that whenever the magnetic flux linked with a closed circuit changes, an emf is induced in it; equivalently, a conductor cutting across field lines develops an induced emf between its ends. The Second Law (quantitative) states that the magnitude of this induced emf equals the rate of change of the linked flux. For a coil of n turns, combining both laws (with Lenz's law fixing the sign) gives $e=-n\frac{d\Phi_B}{dt}$, often called the flux rule.

Magnetic flux itself is defined, for a small area element $d\vec{a}$ in a field $\vec{B}$, as $d\Phi=\vec{B}\cdot d\vec{a}$, generalised to a finite surface by integration, $\Phi=\int_S\vec{B}\cdot d\vec{a}$. Faraday's law in its most general form is therefore $e=-\frac{d}{dt}\int_S\vec{B}(t)\cdot d\vec{a}$ -- the induced emf equals the work done per unit charge in carrying a test charge once around the circuit's boundary, and it can arise from a changing field, a changing circuit area, or both. Faraday's law is the single equation from which every application in this chapter (motional emf, generators, self- and mutual inductance, the transformer) is ultimately derived.