A 30 cm long solenoid has 10 turns per cm and area of $5 \mathrm{~cm}^2$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s . The e.m.f. induced in the coil is $\alpha \times 10^{-5} \mathrm{~V}$. The value $\alpha$ is $\_\_\_\_$ .

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

An inductor of inductance 10 mH having resistance of $100 \Omega$ is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is $\_\_\_\_$ .

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(\mathrm{r})=B_{\mathrm{o}} \mathrm{e}^{-\lambda r} ; \lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :