$A$ circular coil is placed near a current-carrying conductor, both lying on the plane of the paper. The current is flowing through the conductor in such a way that the induced current in the loop is clockwise, as shown in the figure. The current in the wire is,

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8 \ \Omega$ varies with time (in seconds) as $\phi = 5t^2 - 36t + 1$. The induced current in the circuit at $t = 2 \ s$ is . . . . . . $A$.

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

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

The induced emf cannot be produced by:

$A$ 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: