$A$ 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

Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is

$A$ highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in the figure. The ring has a narrow gap of width $d$ in its circumference. The solenoid has a cross-sectional area $A$ and a uniform internal magnetic field of magnitude $B_0$. Starting at $t = 0$,the solenoid current is steadily increased such that the field magnitude at any time $t$ is given by $B(t) = B_0 + \alpha t$,where $\alpha > 0$. Assuming that no charge can flow across the gap,the end of the ring which has an excess of positive charge and the magnitude of the induced e.m.f. in the ring are respectively:

The magnetic field $B$ crossing normally a square metallic plate of area $4\,m^2$ changes with time as shown in the figure. The magnitude of the induced $emf$ in the plate during $t=2\,s$ to $t=4\,s$ is $..........\,mV$.

$A$ coil of $45$ turns and radius $4 \ cm$ is placed in a uniform magnetic field such that its plane is perpendicular to the direction of the field. If the magnetic field increases from $0$ to $0.70 \ T$ at a constant rate in a time interval of $220 \ s$,then the induced emf in the coil is (in $mV$)

$A$ coil having $n$ turns and resistance $R \, \Omega$ is connected with a galvanometer of resistance $4 \, R \, \Omega$. This combination is moved in time $t$ seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is