A coil having area $A_o$ is placed in a magnetic field. The magnetic field is perpendicular to the plane of the coil. When the magnetic field changes from $B_o$ to $4B_o$ in a time interval t, the magnitude of emf induced in the coil will be:

$\frac{3A_oB_o}{t}$

The correct answer is Option (1) → $\frac{3A_oB_o}{t}$

Magnetic flux: $\Phi = B \cdot A_0$

Initial flux: $\Phi_i = B_0 A_0$

Final flux: $\Phi_f = 4B_0 A_0$

Change in flux: $\Delta \Phi = \Phi_f - \Phi_i = (4B_0A_0 - B_0A_0) = 3B_0A_0$

Induced emf: $\mathcal{E} = \frac{\Delta \Phi}{t} = \frac{3B_0 A_0}{t}$

Answer: $\mathcal{E} = \frac{3B_0 A_0}{t}$