The magnetic flux linked with a coil at any instant $t$ is given by $\phi = 5t^3 - 100t + 300$. The $e.m.f.$ induced in the coil at $t = 2 \ s$ is $....... \ V$.

$A$ rectangular coil of $20$ turns and area of cross section $25 \text{ cm}^2$ has a resistance of $100 \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at a rate of $100 \text{ T/s}$, the current in the coil is . . . . . . . (in $\text{ A}$)

$A$ 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 . . . . . . .

$A$ long solenoid has $20$ turns per cm. $A$ small loop of area $\frac{4}{\pi} \text{ cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $1.0 \text{ A}$ to $3.0 \text{ A}$ in $0.2 \text{ s}$,what is the magnitude of the induced emf in the loop while the current is changing (in $\mu \text{V}$)?

$A$ coil of $45$ turns and radius $4 \ cm$ is placed in a uniform magnetic field such that its plane is perpendicular to the direction of the field. If the magnetic field increases from $0$ to $0.70 \ T$ at a constant rate in a time interval of $220 \ s$,then the induced emf in the coil is (in $mV$)

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