$A$ coil is placed in a magnetic field $\vec{B}$ as shown below. $A$ current is induced in the coil because $\vec{B}$ is:

Magnetic flux (in $Wb$) linked with a closed loop varies with time $t$ (in $s$) as $\phi = 2t^2 + 1$. The magnitude of induced emf at $t = 1 \ s$ is $..... \ V$.

$A$ coil of resistance $400 \,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi \,(Wb)$ linked with the coil varies with time $t \,(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \,s$ is.....$A$.

$A$ circular loop of flexible conducting material is kept in a magnetic field directed perpendicularly into its plane. By holding the loop at diametrically opposite points,it is suddenly stretched outwards,then

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

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 . . . . . .