Question

A coil of number of turns $N$, area $A$ is rotated at a constant angular speed $\omega$, in a uniform magnetic field $B$ and connected to a resistor $R$.Deduce expressions for
Maximum emf induced in the oil.
Power dissipation in the coil.

Answer 1

Suppose initially the plane of coil is perpendicular to the magnetic field $B$. When coil rotates with angular speed $\omega$, then after time $t$, the angle between magnetic field $\overrightarrow{B}$ and normal to plane coil is
$\theta =\omega t$
$\therefore$ At this instant magnetic flux linked with the coil $\phi =BA\cos \omega t$
If coil constant, $N-$turns, then emf induced in the coil
$\epsilon =-N\frac{d\phi }{dt}\left(BA\cos \omega t\right)$
$=+NBA\omega \sin \omega t$ ...$\left(i\right)$
$\therefore$ For maximum value of emf $\epsilon$,
$\sin \omega t=1$
$\therefore$ Maximum emf induced, ${\epsilon }_{max}=NBA\omega$