The magnetic field of an electromagnetic wave in a certain region obeys the relation $B = 10^{-12} \sin(5 \times 10^6 t) \text{ T}$,where $t$ is the time. Then,the induced emf in a coil of $300$ turns and area $20 \text{ cm}^2$,oriented perpendicular to the field,is:

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,

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of the cross-sectional area $24\,cm^2$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\,\Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5\,T$ in one direction to $1.5\,T$ in the opposite direction,the charge flowing through a point in the circuit during the change of magnetic field will be $.........\,mC$.

Magnetic flux in a circuit containing a coil of resistance $2\,\Omega$ changes from $2.0\,Wb$ to $10\,Wb$ in $0.2\,s$. The charge passed through the coil in this time is......$C$

$A$ $50$ turns circular coil has a radius of $3\;cm$. It is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increases from $0.10\;T$ to $0.35\;T$ in $2\;ms$. The average induced $e.m.f.$ in the coil is.......$V$.

$A$ current-carrying infinitely long wire is kept along the diameter of a circular wire loop,without touching it. The correct statement$(s)$ is (are):
$(A)$ The emf induced in the loop is zero if the current is constant.
$(B)$ The emf induced in the loop is finite if the current is constant.
$(C)$ The emf induced in the loop is zero if the current decreases at a steady rate.
$(D)$ The emf induced in the loop is finite if the current decreases at a steady rate.