$A$ copper rod is moved in a magnetic field. The charge developed across its ends will be proportional to

As shown in the figure, two identical conducting rings of radius $r$ are placed in a magnetic field. In figure $(a)$, the magnetic field is increasing at the rate of $0.3 \text{ T/s}$, and in figure $(b)$, the magnetic field is decreasing at the rate of $0.2 \text{ T/s}$. The direction of the current in ring $(a)$ and ring $(b)$, when observed from the top, is . . . . . .

$A$ system $S$ consists of two coils $A$ and $B$. The coil $A$ carries a steady current $I$. The coil $B$ is suspended nearby as shown in the figure. If the system is heated,so as to raise the temperature of the two coils steadily,then:

$A$ bar magnet is passing through a conducting loop of radius $R$ with velocity $v$. The radius of the bar magnet is such that it just passes through the loop. The induced $e.m.f.$ in the loop can be represented by the approximate curve:

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 $.........\,mC$.

The magnetic flux linked with a coil (in $Wb$) is given by the equation $\phi = 5t^2 + 3t + 16$. The magnitude of induced emf in the coil at the fourth second will be (in $V$):