$A$ square loop of area $25\,cm^2$ has a resistance of $10\,\Omega$. The loop is placed in a uniform magnetic field of magnitude $40.0\,T$. 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 $1.0\,s$ will be $..........\times 10^{-3}\,J$.

$A$ wheel with $10$ metallic spokes,each $0.5 \ m$ long,is rotated with a speed of $120 \ rev/min$ in a plane normal to the horizontal component of Earth's magnetic field $H_E$ at a place. If $H_E = 0.4 \ G$ at the place,then the induced emf is: $(1 \ G = 10^{-4} \ T)$

$A$ horizontal wire is free to slide on the vertical rails of a conducting frame as shown in the figure. The wire has a mass $m$ and length $l$,and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame,find the terminal speed of the wire as it falls under the force of gravity.

Two long parallel horizontal rails,a distance $l$ apart,each having a resistance $\lambda$ per unit length,are joined at one end by a resistance $R$. $A$ perfectly conducting rod $MN$ of mass $m$ is free to slide along the rails without friction. There is a uniform magnetic field of induction $B$ normal to the plane of the paper and directed into the paper. $A$ variable force $F$ is applied to the rod $MN$ such that,as the rod moves,a constant current $i$ flows through the circuit. The applied force $F$ as a function of distance $x$ of the rod from $R$ is:

$A$ coil of $N$ turns and mean cross-sectional area $A$ is rotating with uniform angular velocity $\omega$ about an axis at right angle to a uniform magnetic field $B$. The induced e.m.f. $E$ in the coil will be

$A$ conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V$. The $emf$ induced in the frame will be proportional to