$A$ circular coil and a bar magnet placed nearby are made to move in the same direction. The coil covers a distance of $1\, m$ in $0.5\, s$ and the magnet covers a distance of $2\, m$ in $1\, s$. The induced emf produced in the coil is.....$V$.

$A$ square coil $ABCD$ is placed in the $x-y$ plane with its centre at the origin. $A$ long straight wire,passing through the origin,carries a current in the negative $z$-direction. The current in this wire increases with time. The induced current in the coil is:

Write down the names of two devices which work on the principle of electromagnetic induction.

In a coil of resistance $100 \ \Omega$,a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is......$Wb$.

$(a)$ $A$ 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.

Two inductor coils of self-inductance $3\,H$ and $6\,H$ respectively are connected with a resistance $10\,\Omega$ and a battery $10\,V$ as shown in the figure. The ratio of the total energy stored at steady state in the inductors to that of the heat developed in the resistance in $10\,s$ at the steady state is (neglect mutual inductance between $L_1$ and $L_2$):-