$A$ square loop of side $0.1 \, m$ and resistance $1 \, \Omega$ is moved with a constant velocity in a magnetic field of $2 \, Wb/m^2$. If a current of $1 \, mA$ is induced in the circuit, what is the velocity of the loop in $cm/sec$? (The external circuit consists of a Wheatstone bridge with five $3 \, \Omega$ resistors as shown in the figure.)

$A$ short magnet is allowed to fall along the axis of a horizontal metallic ring. Starting from rest,the distance fallen by the magnet in one second may be.....$m$

$A$ triangular wire frame (each side $= 2 \, m$) is placed in a region of time-variant magnetic field having $dB/dt = \sqrt{3} \, T/s$. The magnetic field is perpendicular to the plane of the triangle. The base of the triangle $AB$ has a resistance $1 \, \Omega$ while the other two sides have resistance $2 \, \Omega$ each. The magnitude of potential difference between the points $A$ and $B$ will be....$V$

$A$ circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing,the wires remain electrically insulated from each other. The entire loop lies in the plane of the paper. $A$ uniform magnetic field $\vec{B}$ points into the plane of the paper. At $t=0$,the loop starts rotating about the common diameter as an axis with a constant angular velocity $\omega$ in the magnetic field. Which of the following options is/are correct?
[$A$] The rate of change of the flux is maximum when the plane of the loops is perpendicular to the plane of the paper.
[$B$] The net emf induced due to both the loops is proportional to $\cos \omega t$.
[$C$] The emf induced in the loop is proportional to the sum of the areas of the two loops.
[$D$] The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone.

Write down the names of two devices which work on the principle of electromagnetic induction.

Plane figures made of thin wires of resistance $R = 50 \text{ m}\Omega/\text{m}$ are located in a uniform magnetic field perpendicular to the plane of the figures, which decreases at the rate $dB/dt = 0.1 \text{ mT/s}$. Find the currents in the inner and outer boundary. (The inner radius $a = 10 \text{ cm}$ and outer radius $b = 20 \text{ cm}$)