$A$ vertical rod of length $l$ is moved with constant velocity $v$ towards the east. If the vertical component of the Earth's magnetic field is $B$ and the angle of dip is $\theta$,then the induced $emf$ in the rod is:

The figure shows a square loop of side $5 \ cm$ being moved towards the right at a constant speed of $1 \ cm/s$. The front edge enters the $20 \ cm$ wide magnetic field $(B = 0.6 \ T)$ at $t = 0$. Find the $emf$ induced in the loop at $(a) \ t = 2 \ s$,$(b) \ t = 10 \ s$,and $(c) \ t = 22 \ s$.

$A$ bar of mass $m$,length $d$,and resistance $R$ slides without friction in a horizontal plane,moving on parallel rails as shown in the figure. $A$ battery that maintains a constant emf $\varepsilon$ is connected between the rails,and a constant magnetic field $\vec{B}$ is directed perpendicularly to the plane of the page. Assuming the bar starts from rest,find the speed at time $t$.

$A$ long rectangular conducting loop of width '$l$',mass '$m$',and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ($g = $ acceleration due to gravity)

$A$ rectangular loop of length $l$ and breadth $b$ is placed at a distance of $x$ from an infinitely long wire carrying current $i$ such that the direction of the current is parallel to the breadth of the loop. If the loop moves away from the current-carrying wire in a direction perpendicular to it with a velocity $v$,the magnitude of the induced emf in the loop is: ($\mu_0=$ permeability of free space)

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