In the given arrangement,a loop of width $b$ is moved with constant velocity $v$ through a uniform magnetic field $B$ restricted to a region of width $a$ (where $b > a$). The total time for which an $emf$ is induced in the circuit is:

$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

Explain the motional $emf$ by the Lorentz force acting on the free charge carriers of a conductor.

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

$A$ rectangular loop with a sliding connector of length $l = 1.0 \, m$ is situated in a uniform magnetic field $B = 2 \, T$ perpendicular to the plane of the loop. The resistance of the connector is $r = 2 \, \Omega$. Two resistors of $6 \, \Omega$ and $3 \, \Omega$ are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity $v = 2 \, m/s$ is ........ $N$.