A coil having effective area ' \(\mathrm{A}\) ' is held with its plane normal to a magnitude field of induction ' \(\mathrm{B}\) '. The magnetic induction is quickly reduced to \(25 \%\) of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

The formula for induced emf is \(\mathrm{e}=\frac{\Delta \phi}{\Delta t}\), where \(\phi=\mathrm{BA}\)
Here, the area is constant and the magnetic field is changing.
\(\begin{aligned}
& \therefore \quad \Delta \phi=\Delta B A \\
& \therefore \quad \Delta \phi=A \cdot \Delta B \\
& \therefore \quad \Delta B=B_1-B_2 \\
& \quad B_1=B \text { and } B_2=\frac{25}{200} B=\frac{1}{4} B \\
& \therefore \quad B=B-\frac{1}{4} B \\
& \therefore \quad B=\frac{3}{4} B
\end{aligned}\)
Substituting the values,
\(\begin{aligned}
\mathrm{e} & =\frac{\Delta \phi}{\Delta \mathrm{t}} \\
\mathrm{e} & =\frac{\mathrm{A} \times \frac{3}{4} \mathrm{~B}}{1} \\
\therefore \quad \mathrm{e} & =\frac{3}{4} \mathrm{AB}
\end{aligned}\)