$A$ square loop of side $1 \, m$ is placed in a perpendicular magnetic field. Half of the area of the loop is inside the magnetic field. $A$ battery of $emf$ $10 \, V$ and negligible internal resistance is connected in the loop. The magnetic field changes with time according to the relation $B = (0.01 - 2t) \, Tesla$. The resultant $emf$ in the loop will be.....$V$

$A$ magnet is made to oscillate with a particular frequency,passing through a coil as shown in the figure. The time variation of the magnitude of $e.m.f.$ generated across the coil during one cycle is

$A$ square loop of side $2 \,cm$ enters a magnetic field with a constant speed of $2 \,cm \,s^{-1}$ as shown. The front edge enters the field at $t=0 \,s$. Which of the following graphs correctly depicts the induced emf in the loop? (Take clockwise direction as positive)

The magnetic field varies as $B = B_0 e^{-t}$. The coil has a radius $r$ and resistance $R$. What is the power dissipated when the key $K$ is closed at $t = 0$?

$(a)$ $A$ closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets?
$(b)$ $A$ closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop
$\quad (i)$ when it is wholly inside the region between the capacitor plates
$\quad (ii)$ when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop.
$(c)$ $A$ rectangular loop and a circular loop are moving out of a uniform magnetic field region to a field-free region with a constant velocity $v$. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops.
$(d)$ Predict the polarity of the capacitor in the situation described by the figure.

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