$A$ square-shaped wire loop of mass $m$,resistance $R$,and side $a$ moving with speed $v_{0}$,parallel to the $X$-axis,enters a region of uniform magnetic field $B$,which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x$ $(x < a)$ in the field as:

$A$ conducting wire bent in the shape of a semicircle has length $L$ and moves in its plane with constant velocity $v$. $A$ uniform magnetic field $B$ exists in the direction perpendicular to the plane of the wire. The velocity makes an angle $45^{\circ}$ to the diameter joining the free ends,and the emf induced between the ends of the wire is $\Phi = \alpha(B v L)$. The value of the constant $\alpha$ is

In the given branch $AB$ of a circuit,a current $I = (10t + 5) \, A$ is flowing,where $t$ is time in seconds. At $t = 0$,the potential difference between points $A$ and $B$ $(V_A - V_B)$ is.....$V$.

Consider the situation shown in the figure. The wires $P_1Q_1$ and $P_2Q_2$ are made to slide on the rails with the same speed $5\, cm/s$. Find the electric current in the $9\,\Omega$ resistor if $(a)$ both the wires move towards the right and $(b)$ if $P_1Q_1$ moves towards the left but $P_2Q_2$ moves towards the right.

$A$ 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:

$A$ jet plane is travelling towards the west at a speed of $1800\, km/h$. What is the voltage difference developed between the ends of the wing having a span of $25\, m$,if the Earth's magnetic field at the location has a magnitude of $5 \times 10^{-4}\, T$ and the dip angle is $30^{\circ}$?