1. Magnetic flux through the rotating coil

For a coil of:

• area $A$
• number of turns $n$
• placed in uniform magnetic field $B$

if it rotates with angular velocity $\omega$, the angle between the normal to the coil and the magnetic field changes as

$\theta = \omega t$

So the magnetic flux through the coil at time $t$ is

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

2. Induced e.m.f. using Faraday's law

Faraday's law gives

$e = -\frac{d\Phi}{dt}$

Therefore,

$e = -\frac{d}{dt}\big(nBA\cos(\omega t)\big)$

$e = -nBA\big(-\omega \sin(\omega t)\big)$

$e = nBA\omega \sin(\omega t)$

3. Maximum induced e.m.f.

The maximum value of $\sin(\omega t)$ is $1$.

Hence,

$e_{\max} = nBA\omega$

4. Match with the options

• A: $3nBA\omega$ ❌
• B: $\dfrac{3}{2}nBA\omega$ ❌
• C: $nBA\omega$ ✅
• D: $\dfrac{1}{2}nBA\omega$ ❌

So the correct option is C.