$A$ coil of effective area $3 \,m^2$ is placed at right angles to a magnetic field of induction $0.05 \,Wb/m^2$. If the field is decreased to $20 \%$ of its original value in $10 \,s$, the e.m.f. induced in the coil will be: (in $\,mV$)

$A$ uniform magnetic field $\vec{B}$ is perpendicular to the plane of a circular loop of diameter $10 \text{ cm}$ formed from a wire of diameter $2 \text{ mm}$ and resistivity $2 \times 10^{-8} \Omega \text{ m}$. If a current of $11 \text{ A}$ is to be induced in the loop, then the rate at which $\vec{B}$ is to be changed is: (in $\text{ T s}^{-1}$)

The north pole of a long horizontal bar magnet is being brought towards a closed circuit consisting of a coil. The direction of the induced current produced in it is

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\Phi_1$ to $\Phi_2$. The induced current in the circuit is:

The magnetic flux linked with a coil satisfies the relation $\phi = 4t^2 + 6t + 9 \text{ Wb}$, where $t$ is the time in seconds. The emf induced in the coil at $t = 2 \text{ s}$ is (in $\text{ V}$)

$A$ 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: