$A$ conducting circular loop is placed in a uniform magnetic field of $0.4\,T$ with its plane perpendicular to the field. The radius of the loop starts expanding at a constant rate of $1\,mm/s$. The magnitude of the induced emf in the loop at an instant when the radius of the loop is $2\,cm$ will be $...........\,\mu V$.

Two $U$-shaped tubes are moving inside each other as shown in the figure. If the length of each tube is $l$ and they move with velocity $v$ in a magnetic field $B$,what is the induced $emf$ in the circuit?

$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

An aeroplane,with its wings spread $10 \, m$,is flying at a speed of $180 \, km/h$ in a horizontal direction. The total intensity of the Earth's magnetic field at that location is $2.5 \times 10^{-4} \, Wb/m^2$ and the angle of dip is $60^{\circ}$. The $EMF$ induced between the tips of the plane's wings will be ...... $mV$.

An equilateral triangular loop $ADC$ moves out of a finite magnetic field $B$ as shown in the figure. At time $t = 0$, side $DC$ of the loop is at the edge of the magnetic field. The magnetic field is perpendicular to the paper inwards (or perpendicular to the plane of the coil). The induced current versus time graph will be as: