$A$ conductor $ABOCD$ moves along its bisector with a velocity of $1\, m/s$ through a perpendicular magnetic field of $1\, wb/m^2$,as shown in the figure. If all the four segments $(OB, BC, OC, CD)$ are of $1\, m$ length each,then the induced emf between points $A$ and $D$ is......$volt$.

$A$ solid metal cube of edge length $2\, cm$ is moving in a positive $y-$ direction at a constant speed of $6\, m/s$. There is a uniform magnetic field of $0.1\, T$ in the positive $z-$ direction. The potential difference between the two faces of the cube perpendicular to the $x-$ axis is.....$mV$.

$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced $emf$ in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

$A$ square loop of area $25 \, cm^2$ has a resistance of $10 \, \Omega$. The loop is placed in a uniform magnetic field of magnitude $40 \, T$. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1 \, s$ will be:

In the figure shown, the conductor $PQ$ of length $l$ is moved from $x = 0$ to $x = b$ and then up to $x = 2b$ with a constant velocity $\vec{v}$. $A$ uniform magnetic field $\vec{B}$ is perpendicular to the plane of the paper and extends from $x = 0$ to $x = b$, and it is zero for $x > b$. The magnitude of the emf induced in the conductor is:

$A$ square-shaped conducting wire loop of dimension $a$ moving parallel to the $X$-axis approaches a square region of size $b$ $(a < b)$,where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region,the plot correctly depicting its speed $v$ as a function of $x$ is