$A$ square loop of side $10 \ cm$ and resistance $0.7 \ \Omega$ is placed vertically in the east-west plane. $A$ uniform magnetic field of $0.20 \ T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $1 \ s$ at a steady rate. Then,the magnitude of the induced emf is $\sqrt{x} \times 10^{-3} \ V$. The value of $x$ is . . . . . . .

The magnetic flux linked with a coil varies with time as $\Phi = 4t^2 + 3t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)

The magnitude of induced emf is directly proportional to the rate of change of magnetic flux linked with the coil. This statement is known as

The magnetic flux through a coil of resistance $10\,\Omega$ changes. As a result,an induced current is developed in it,which varies with time as shown in the figure. The magnitude of the change in magnetic flux through the coil in webers is:

The magnetic flux linked with a coil,in weber,is given by the equation $\phi = 5t^2 + 3t + 16$. The induced emf in the coil in the fourth second is.....$V$

$A$ 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: