$A$ rectangular conducting loop of sides $8\, cm$ and $2\, cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3\, T$ directed normal to the loop as shown in figures $(i)$ and $(ii)$. If the velocity of the loop is $1\, cm\, s^{-1}$,then the ratio of the voltage developed across $ab$ in case $(i)$ to case $(ii)$ is:

The magnetic field in a region is given by $\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }$. $A$ square loop of side $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{ v }= v _{0} \hat{ i }$. The emf induced in the loop is:

$A$ region in the form of an equilateral triangle (in $x-y$ plane) of height $L$ has a uniform magnetic field $\vec{B}$ pointing in the $+z$-direction. $A$ conducting loop $PQR$,in the form of an equilateral triangle of the same height $L$,is placed in the $x-y$ plane with its vertex $P$ at $x=0$ in the orientation shown in the figure. At $t=0$,the loop starts entering the region of the magnetic field with a uniform velocity $\vec{v}$ along the $+x$-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graphs best depicts the variation of the induced emf $(E)$ in the loop as a function of the distance $(x)$ starting from $x=0$?

$A$ simple pendulum with a bob of mass $m$ and a conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of the Earth's magnetic field in the direction perpendicular to the swing is $B$. The maximum e.m.f. induced across the pendulum is ($g=$ acceleration due to gravity).

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?

$A$ long,rectangular conducting loop of width $l$,mass $m$,and resistance $R$ is placed partly in a perpendicular magnetic field $B$. It is pushed downwards with velocity $v$ so that it may continue to fall freely. The velocity $v$ is ($g=$ acceleration due to gravity).