The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = (2t^2 + 4t + 6) \, mWb$. The $emf$ induced in the loop at $t = 4 \, s$ is ....... $V$.

The phenomenon of "Electromagnetic induction" was discovered by which scientist?

$A$ metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t = 0$ and completely emerges out at $t = T \, \text{sec}$. The current in the ring varies as

$A$ long solenoid of diameter $0.1\, m$ has $2 \times 10^4$ turns per meter. At the centre of the solenoid,a coil of $100$ turns and radius $0.01\, m$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0\, A$ from $4\, A$ in $0.05\, s$. If the resistance of the coil is $10\pi^2\, \Omega$,the total charge flowing through the coil during this time is:

$A$ rectangular loop of wire $ABCD$ is kept close to an infinitely long wire carrying a current $I(t) = I_0(1 - t/T)$ for $0 \le t \le T$ and $I(t) = 0$ for $t > T$ as shown in the figure. Find the total charge passing through a given point in the loop in time $T$. The resistance of the loop is $R$.

$A$ square loop of side $10 \ cm$ and resistance $0.5 \ \Omega$ is placed vertically in the east-west plane. $A$ uniform magnetic field of $0.10 \ T$ is set across the plane in the north-east direction. The magnetic field decreases to zero at $0.70 \ s$ at a steady rate. Then the magnitude of the induced current during this time interval will be . . . . . . .