$A$ conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. $A$ magnetic induction $B$ constant in time and space,pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field,as shown in figure. The induced $e.m.f.$ is

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m$,each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T$. $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? ..... $m/s$ (Neglect self-inductance of the loop)

$A$ horizontal straight wire $10 \; m$ long extending from east to west is falling with a speed of $5.0 \; m \, s^{-1}$,at right angles to the horizontal component of the earth's magnetic field,$0.30 \times 10^{-4} \; Wb \, m^{-2}$.
$(a)$ What is the instantaneous value of the $emf$ induced in the wire?
$(b)$ What is the direction of the $emf$?
$(c)$ Which end of the wire is at the higher electrical potential?

An aeroplane is travelling horizontally towards west with a speed of $540 \,km/h$. The wing span of the plane is $20 \,m$. If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$, the potential difference developed between the ends of the wing is (in $\,V$)

$A$ small rectangular loop of wire in the plane of the paper is moved with uniform speed across a limited region of uniform magnetic field perpendicular to the plane of the paper as shown below. Which graph would best represent the variation of the electric current $I$ in the wire with time $t$?

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: