$A$ rectangular loop $PQRS$ is being pulled with a constant speed into a uniform transverse magnetic field by a force $F$ (as shown). The $e.m.f.$ induced in side $PS$ and the potential difference between points $P$ and $S$ respectively are (Resistance of the loop $= r$)

$A$ wire of mass $m$ and length $l$ can slide freely on a pair of smooth,vertical rails (figure). $A$ magnetic field $B$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance $C$. The acceleration of the wire,neglecting any electric resistance,is:

$A$ long horizontal metallic rod with length along the east-west direction is falling under gravity. The potential difference between its two ends will

$A$ 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?

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:

$A$ square frame of metallic wire is moving in a uniform magnetic field $(\vec{B})$ acting perpendicular to the paper inward as shown. $LP$ and $QN$ are also metallic wires. Find the potential difference between $L$ and $N$.