Question

When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its center and perpendicular to the field, the emf induced in the coil varies_______

• A. linearly
• B. exponentially
• C. sinusoidally
• D. laterally

Answer 1

Answer: (C)

When a rectangular coil is rotated in a uniform magnetic field about an
axis passing through its center and perpendicular to field, then magnetic
flux associated with coil is given as
$\varphi=B A \cos \theta=B A \cos \omega t \ldots$ (i)
$\therefore $ Induced emf, $e=-\frac{d \varphi}{d t}=-\frac{d}{d t} B A \cos \omega t$
[From Eq. (i)]
$=+B A \omega \sin \omega t$
$\Rightarrow e=e_{0} \sin \omega t \ldots$ (ii)
where, $e_{0}$ is the peak value of induced emf.
i.e. $e_{0}=B A \omega$
From Eq. (ii) it is clear that, induced emf varies sinusoidally.