The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \ T$ and the dip is $\tan^{-1}(4/3)$. $A$ thin metal rod of length $0.25 \ m$ placed in the north-south position is moved at a constant speed of $10 \ cm/s$ towards the east. Find the $e.m.f.$ induced in the rod across its ends in $\mu V$.

$A$ rod of length $l$ rotates with a uniform angular velocity $\omega$ about an axis passing through its middle point but normal to its length in a uniform magnetic field of induction $B$ with its direction parallel to the axis of rotation. The induced $emf$ between the two ends of the rod 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:

Initially,a rectangular coil with its length vertical is moving out with a constant velocity $v$ in a constant magnetic field $B$ towards the right. Now,the same coil is rotated through $90^{\circ}$ in the same plane in the same magnetic field $B$,and the coil is moving with the same velocity $v$. The magnitude of the induced e.m.f. is now

$A$ 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 $x=0$?

$A$ metal rod of length $2 \, m$ is rotating with an angular velocity of $100 \, rad/s$ in a plane perpendicular to a uniform magnetic field of $0.3 \, T$. The potential difference between the ends of the rod is.......$V$