$A$ rectangular coil of $20$ turns and area of cross section $25 \text{ cm}^2$ has a resistance of $100 \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at a rate of $100 \text{ T/s}$, the current in the coil is . . . . . . . (in $\text{ A}$)

$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \,cm^2$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \,A$ to $4.0 \,A$ in $0.1 \,s$, the induced emf in the loop while the current is changing is nearly [Take $\pi=3.14$].

The formula for induced $e.m.f.$ in a coil due to change in magnetic flux through the coil is (here $A$ = area of the coil,$B$ = magnetic field).

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments $ab$ and $cd$. Then,

$A$ circular coil of area $100 \,cm^2$ and $20$ turns is kept in a magnetic field of flux density $2 \,Wb/m^2$. It rotates from a position where its plane makes an angle of $30^{\circ}$ with the field to a position perpendicular to the field in a time $0.2 \,s$. Find the magnitude of the emf induced in the coil due to its rotation. (in $V$)

$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \; cm^{2}$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \; A$ to $4.0 \; A$ in $0.1 \; s$, what is the induced $emf$ in the loop while the current is changing?