$A$ vertical bar magnet is dropped from the shown position on the axis of a fixed metallic coil as shown in Fig-$I$. In Fig-$II$,the magnet is fixed and a horizontal coil is dropped. If the acceleration of the magnet and coil are $a_1$ and $a_2$ respectively,then:

The coil and magnet are moved in the same direction with the same speed $V$. The induced e.m.f. is

Suppose a long solenoid of $100 \ cm$ length,radius $2 \ cm$ having $500 \ turns/cm$ carries a current $I = 10 \sin(\omega t) \ A$,where $\omega = 1000 \ rad/s$. $A$ circular conducting loop $(B)$ of radius $1 \ cm$ is coaxially placed inside the solenoid. The r.m.s. current through the loop when the coil $B$ is inside the solenoid is $\alpha / \sqrt{2} \ \mu A$. The value of $\alpha$ is . . . . . . . [Resistance of the loop $= 10 \ \Omega$]

$A$ magnetic field of flux density $1.0 \,Wb \,m^{-2}$ acts normal to a $80$ turn coil of $0.01 \,m^2$ area. If this coil is removed from the field in $0.2 \,s$, then the emf induced in it is (in $\,V$)

$A$ circular loop of radius $7 \ cm$ is placed in a uniform magnetic field of $0.2 \ T$ directed perpendicular to the plane of the loop. The loop is converted into a square loop in $0.5 \ s$. The $EMF$ induced in the loop is . . . . . . $mV$.

$A$ coil has an area $0.06 \ m^2$ and it has $600$ turns. After placing the coil in a magnetic field of strength $5 \times 10^{-5} \ Wb/m^2$,it is rotated through $90^{\circ}$ in $0.2 \ s$. The magnitude of average e.m.f induced in the coil is