A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $$B = 0.4 \sin(300t)$$ Tesla. The normal to the plane of loop makes an angle of $$60°$$ with the field. The maximum induced emf produced in the loop is __________ mV.

$$\text{emf} = -\frac{d\Phi}{dt}$$

$$\Phi = B \cdot A \cdot \cos\theta$$

$$\Phi = [0.4\sin(300t)] \times (4 \times 10^{-4}) \times \cos(60^\circ)$$

$$\Phi = 1.6 \times 10^{-4} \sin(300t) \times \frac{1}{2} = 0.8 \times 10^{-4}\sin(300t)$$

$$\text{emf} = \frac{d\Phi}{dt} = 0.8 \times 10^{-4} \times \cos(300t) \times 300$$

$$\text{emf} = 0.024\cos(300t)\text{ V}$$

$$\text{emf}_{\max} = 0.024\text{ V}$$

$$\text{emf}_{\max} = 0.024 \times 10^3\text{ mV} = 24\text{ mV}$$