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?

Find the current in the wire for the configuration shown in the figure. Wire $PQ$ has negligible resistance. $\vec{B}$ is the magnetic field coming out of the paper. $\theta$ is a fixed angle made by $PQ$ as it travels smoothly over two conducting parallel wires separated by a distance $d$.

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ directed into the plane of the paper (See figure). If charge densities $\sigma_1$ and $\sigma_2$ are induced on the left and right surfaces,respectively,of the sheet,then (ignore fringe effects):

$A$ big circular coil of $1000$ turns and average radius $10 \, m$ is rotating about its horizontal diameter at $2 \, rad \cdot s^{-1}$. If the vertical component of Earth's magnetic field at that place is $2 \times 10^{-5} \, T$ and the electrical resistance of the coil is $12.56 \, \Omega$,then the maximum induced current (in $A$) in the coil will be:

$A$ rod of length $l$ is rotating with constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of rotation. The rod is marked at points $0, 1, 2, \dots, 8$ at equal spacing. What is the nature of the potential difference between consecutive points as we move from left to right?

$A$ frame $CDEF$ is placed in a region where a magnetic field $\vec{B}$ is present. $A$ rod $PQ$ of length $l = 1 \, m$ moves with a constant velocity $v = 20 \, m/s$ and the strength of the magnetic field is $B = 1 \, T$. The power spent in the process is .............. $kW$ (take $R = 0.2 \, \Omega$ and assume all other wires and the rod have zero resistance).