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 of radius $2\, cm$ has $100\, turns/cm$ and carries a current of $5\, A$. $A$ coil of radius $1\, cm$ having $100\, turns$ and a total resistance of $20\, \Omega$ is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction,find the charge flown through the galvanometer.

$A$ uniform magnetic field is restricted within a region of radius $r$. The magnetic field changes with time at a rate $\frac{d\vec{B}}{dt}$. Loop $1$ of radius $R > r$ encloses the region,and loop $2$ of radius $R$ is outside the region of the magnetic field as shown in the figure. Then the $e.m.f.$ generated is:

There are two coils $A$ and $B$ as shown in the figure. No current flows in $B$ if $A$ is at rest. Now,the coil $A$ is made to rotate about a vertical axis. At the shown instant $(t=0)$,what will be the direction of the current in coil $A$,when the induced current in coil $B$ is counterclockwise?

The total emf induced in a closely wound coil of $N$ turns in which the magnetic flux linked with the coil is changing at the rate $\frac{d \phi_{B}}{dt}$ is

$A$ conducting loop is kept perpendicularly in an increasing magnetic field,as shown in the figure. The direction of the induced current in the loop will be: