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 ..... $V$.

$A$ 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:

$A$ copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ($g=$ acceleration due to gravity)

$A$ 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:

If magnetic flux $\phi = (3t^2 - 2t + 5) \ Wb$,then what is the induced emf at $t = 2 \ s$?

The magnetic flux through a coil is $4 \times 10^{-4} \ Wb$ at time $t=0$. It reduces to $30 \%$ of its original value in time $t$ seconds. If the e.m.f. induced in the coil is $0.56 \ mV$,then the value of $t$ is: (in $s$)