The figure shows four wire loops,with edge lengths of either $L$ or $2L$. All four loops move through a region of uniform magnetic field (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the electromotive force (e.m.f.) induced as they move through the field,greatest first.

$A$ conducting wire of parabolic shape,initially $y=x^2$,is moving with velocity $\vec{V} = V_0 \hat{i}$ in a non-uniform magnetic field $\vec{B} = B_0 \left(1 + \left(\frac{y}{L}\right)^\beta\right) \hat{k}$,as shown in the figure. If $V_0, B_0, L$ and $\beta$ are positive constants and $\Delta \phi$ is the potential difference developed between the ends of the wire,then the correct statement$(s)$ is/are:
$(1)$ $|\Delta \phi|$ remains the same if the parabolic wire is replaced by a straight wire,$y=x$ initially,of length $\sqrt{2} L$.
$(2)$ $|\Delta \phi|$ is proportional to the length of the wire projected on the $y$-axis.
$(3)$ $|\Delta \phi| = \frac{1}{2} B_0 V_0 L$ for $\beta = 0$.
$(4)$ $|\Delta \phi| = \frac{4}{3} B_0 V_0 L$ for $\beta = 2$.

$A$ boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \text{ T}$ and is directed due north and horizontal. The boat carries a vertical aerial $2 \text{ m}$ long. If the speed of the boat is $1.5 \text{ m/s}$,calculate the magnitude of the induced $emf$ in the aerial wire in $mV$.

$A$ rectangular wire loop of sides $8 \;cm$ and $2 \;cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \;T$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 \;cm \,s^{-1}$ in a direction normal to the $(a)$ longer side,$(b)$ shorter side of the loop? For how long does the induced voltage last in each case?

$A$ copper rod $AB$ of length $L$,pivoted at one end $A$,rotates at a constant angular velocity $\omega$,at right angles to a uniform magnetic field of induction $B$. The e.m.f. developed between the midpoint $C$ of the rod and end $B$ is

$A$ circular coil of $500$ turns encloses an area of $0.04 \,m^2$. $A$ uniform magnetic field of induction $0.25 \,Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1 \,s$ at a constant angular velocity about one of its diameters. $A$ galvanometer of resistance $25 \,\Omega$ is connected in series with the coil. The total charge that will pass through the galvanometer is.......$C$