$A$ $50$ turns circular coil has a radius of $3\;cm$. It is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increases from $0.10\;T$ to $0.35\;T$ in $2\;ms$. The average induced $e.m.f.$ in the coil is.......$V$.

Two coaxial coils carry current in the same direction. When the distance between the two coils is increased,the electric current in the coils will:

$A$ circular loop of radius $7 \ cm$ is placed in a uniform magnetic field of $0.2 \ T$ directed perpendicular to the plane of the loop. The loop is converted into a square loop in $0.5 \ s$. The $EMF$ induced in the loop is . . . . . . $mV$.

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

$A$ 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:

The following figure shows planar loops of different shapes moving into or out of a region of a magnetic field which is directed normal to the plane of the loop,away from the reader. Determine the direction of the induced current in each loop using Lenz's law.