The magnetic flux through a coil is $4 \times 10^{-4} \ Wb$ at time $t=0$. It reduces to $30 \%$ of its original value in time $t$ seconds. If the e.m.f. induced in the coil is $0.56 \ mV$,then the value of $t$ is: (in $s$)

$A$ long solenoid having $100$ turns per $cm$ carries a current of $\frac{4}{\pi} \,A$. At the centre of it is placed a coil of $200$ turns of cross-sectional area $25 \,cm^2$ having its axis parallel to the field produced by the solenoid. When the direction of the current in the solenoid is reversed within $0.04 \,s$, the induced emf in the coil is (in $\,V$)

In the arrangement shown in the given figure,the current from $A$ to $B$ is increasing in magnitude. The induced current in the loop will

As a result of a change in the magnetic flux linked to the closed loop as shown in the figure,an $e.m.f.$ $V$ volt is induced in the loop. The work done (in joule) in taking a charge $Q$ coulomb once along the loop is

$A$ 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,

If a coil of $40$ turns and area $4 \, cm^2$ is suddenly removed from a magnetic field,it is observed that a charge of $2 \times 10^{-4} \, C$ flows through the coil. If the resistance of the coil is $80 \, \Omega$,the magnetic flux density in $Wb \, m^{-2}$ is: