Question

A coil of mean area $500\, cm ^{2}$ and having $1000$ turns is held perpendicular to a uniform field of $0.4$ gauss. the coil is turned through $180^{\circ}$ in $1 / 10$ second. The average induced emf (in $V$ ) is_____.

Answer 1

When the plane of coil is perpendicular to field, the angle between area $\vec{A}$ and field $\vec{B}$ is $0^{\circ}$.
The flux linked with coil $\phi_{1}=N B A \cos 0=N B A$.
When coil is turned through $180^{\circ}$, the flux linked $\phi_{2}=N B A \cos \pi=-N B A$
$\therefore$ Change in flux $\phi=\phi_{2}-\phi_{1}=-2 N B A$
The magnitude of the induced emf is
$\varepsilon=-\frac{d \phi}{d t}=\frac{2 N B A}{d t}$
$=\frac{2 \times 1000 \times 0.4 \times 10^{-4} \times 500 \times 10^{-4}}{0.1}$
$=0.04\, V$