The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi = (5t^3 + 4t^2 + 2t - 5) \; Wb$. If the resistance of the coil is $5 \; \Omega$,then the induced current through the coil at $t = 2 \; s$ will be $.... \; A$. (in $.6$)

$A$ long solenoid of diameter $0.1\, m$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid,a coil of $100$ turns and radius $0.01\, m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0\, A$ from $4\, A$ in $0.05\, s$. If the resistance of the coil is $10\pi^2\, \Omega$,the total charge flowing through the coil during this time is:

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 $V$):

In the above diagram,a strong bar magnet is moving towards solenoid-$2$ from solenoid-$1$. The direction of induced current in solenoid-$1$ and that in solenoid-$2$,respectively,are through the directions:

The figure shows the north pole of a magnet moving away from a thick conducting loop containing a capacitor. The excess positive charge will arrive on

The adjoining figure shows two different arrangements in which two square wire frames are placed in a uniform constantly decreasing magnetic field $B.$ The direction of induced current in the case $II$ is