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
$\phi =BA\cos \theta =BA\cos \omega t\dots$ (i)
$\therefore$ Induced emf, $e=-\frac{d\phi }{dt}=-\frac{d}{dt}BA\cos \omega t$
[From Eq. (i)]
$=+BA\omega \sin \omega t$
$\Rightarrow e=e_0\sin \omega t\dots$ (ii)
where, $e_0$ is the peak value of induced emf.
i.e. $e_0=BA\omega$
From Eq. (ii) it is clear that, induced emf varies sinusoidally.