Question

(a) Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of magnetic field $\overrightarrow{B}$ .
(b) A horizontal conducting rod 10 m long extending from east to west is falling with a speed 5.0 $m{s}^{-1}$ at right angles to the horizontal component of the Earth's magnetic field, $0.3\times {10}^{-4}Wb{m}^{-2}$. Find the instantaneous value of the emf induced in the rod.

Answer 1

(a) If N is the number of turns in coil, A the area of coil and B the magnetic induction , then flux $\varphi$ linked with the coil is given by
$\varphi =B.A$
$\varphi =B.Acos\omega t$
The e.m.f induced in the coil is given by
$e=-N\frac{d\varphi }{dt}$
$e=-N\frac{d}{dt}\left(BAcos\omega t\right)$
$e=+NBA\omega sin\omega t$
$e=e_{0}sin\omega t$
Where $e_0=NAB\omega$
(b) $e=B_{H}l\upsilon$
$=0.3\times {10}^{-4}\times 10\times 5$
$e=15\times {10}^{-4}V$