Q.(a) Discuss with theory the method of inducing emf in a coil by changing its orientation with respect to the direction of the magnetic field. OR

(a) Rotating a coil in a uniform magnetic field changes the flux linkage sinusoidally, inducing a sinusoidal alternating emf $e=e_0\sin\omega t$ — this is the working principle of an AC generator. (b) A half-wave rectifier uses one diode's one-way conduction to pass only alternate half-cycles of an AC input, producing a pulsating unidirectional output. Both alternatives are answered in full below.

(a) Induced emf by changing the orientation of a coil (AC generator)

Consider a rectangular coil of $N$ turns and area $A$, mounted so that it can rotate about an axis perpendicular to a uniform magnetic field $\vec B$, with constant angular velocity $\omega$. Let $\theta$ be the angle between the normal to the coil and $\vec B$ at time $t$; if the coil starts in the plane of $B$ (normal aligned with $B$) at $t=0$, then $\theta = \omega t$.

The magnetic flux linked with the coil at time $t$ is

$\Phi(t) = NBA\cos\theta = NBA\cos\omega t$

By Faraday's law of electromagnetic induction, the induced emf is

$e = -\dfrac{d\Phi}{dt} = -NBA\dfrac{d}{dt}(\cos\omega t) = NBA\omega\sin\omega t$

Writing $e_0 = NBA\omega$ (the peak/maximum emf), this is

$e = e_0\sin\omega t$

So as the coil's orientation with respect to $\vec B$ changes continuously due to rotation, the flux through it varies sinusoidally, and by Faraday's law this induces a sinusoidally alternating emf — reversing direction every half rotation. This is exactly the working principle of an AC generator (alternator): mechanical rotation of a coil (armature) in a magnetic field (produced by field magnets) is converted to alternating emf, collected via slip rings and brushes and delivered to an external circuit.

(b) Half-wave rectifier

A p-n junction diode conducts current easily when forward biased (p-side at higher potential) and blocks current (except a negligible reverse saturation current) when reverse biased. This one-way conduction property is used to convert AC to a unidirectional (pulsating) output.

Circuit: The AC supply is fed to the primary of a step-down transformer; the secondary is connected in series with a diode $D$ and a load resistor $R_L$, forming a closed loop.

…