$A$ square frame of side $10\, cm$ and a long straight wire carrying current $1\, A$ are in the plane of the paper. Starting from close to the wire,the frame moves towards the right with a constant speed of $10\, ms^{-1}$ (see figure). The $e.m.f.$ induced at the time the left arm of the frame is at $x = 10\, cm$ from the wire is .....$\mu V$.

$A$ 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

$A$ 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 $t$.

$A$ wire $cd$ of length $l$ and mass $m$ is sliding without friction on conducting rails $ax$ and $by$ as shown. The vertical rails are connected to each other with a resistance $R$ between $a$ and $b$. $A$ uniform magnetic field $B$ is applied perpendicular to the plane $abcd$ such that $cd$ moves with a constant velocity $v$. Find the value of $v$.

The magnetic field in a region is given by $\vec B = B_0(1 + \frac{x}{a})\hat k$. $A$ square loop of edge length $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec V = V_0\hat i$. The $emf$ induced in the loop is:

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?