The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

$A$ long straight wire is parallel to one edge of a rectangular loop as shown in the figure. If the current in the long wire varies with time as $I = I_0 e^{-t/\tau}$,what will be the induced $emf$ in the loop?

$A$ dynamo is a device for converting:

As per the given figure,if $\frac{ dI }{ dt } = -1 \text{ A/s}$,then the value of $V_{AB}$ at this instant will be $.......... \text{ V}$.

$A$ coil having $N$ turns and resistance $R$ $\Omega$ is connected to a galvanometer of resistance $6R$ $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time $t$ second. The induced current in the circuit is

$A$ rectangular loop of sides $12 \text{ cm}$ and $5 \text{ cm}$,with its sides parallel to the $x$-axis and $y$-axis respectively,moves with a velocity of $5 \text{ cm/s}$ in the positive $x$-axis direction in a space containing a variable magnetic field in the positive $z$-direction. The field has a gradient of $10^{-3} \text{ T/cm}$ along the negative $x$-direction and it is decreasing with time at the rate of $10^{-5} \text{ T/s}$. If the resistance of the loop is $6 \text{ m}\Omega$,the power dissipated by the loop as heat is . . . . . . $\times 10^{-9} \text{ W}$.