$A$ bar magnet is passing through a conducting loop of radius $R$ with velocity $v$. The radius of the bar magnet is such that it just passes through the loop. The induced $e.m.f.$ in the loop can be represented by the approximate curve:

$A$ circular coil of area $2 \text{ cm}^2$ is placed in a magnetic field of $3 \text{ T}$ perpendicularly. The coil has $10$ turns and $5 \text{ } \Omega$ resistance. Now,the coil is removed from the magnetic field in $0.2 \text{ s}$. The value of induced charge flowing through the coil is . . . . . . .

Assertion : An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.
Reason : The above statement is in accordance with the conservation of energy.

The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = 5t^2 + 10t + 5$ milliweber. The $e.m.f.$ induced in the loop after $5 \, s$ is ..... $V$.

$A$ space consists of two uniform magnetic fields,as shown. $A$ conducting circular loop is placed symmetrically at the boundary.

$A$ highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in the figure. The ring has a narrow gap of width $d$ in its circumference. The solenoid has a cross-sectional area $A$ and a uniform internal magnetic field of magnitude $B_0$. Starting at $t = 0$,the solenoid current is steadily increased such that the field magnitude at any time $t$ is given by $B(t) = B_0 + \alpha t$,where $\alpha > 0$. Assuming that no charge can flow across the gap,the end of the ring which has an excess of positive charge and the magnitude of the induced e.m.f. in the ring are respectively: