$A$ 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 rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\overrightarrow B$ at speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 2\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\,\mu F$ is connected as shown in the figure. Then

$A$ wheel of $20$ metallic spokes,each $40 \text{ cm}$ long,is rotated with a speed of $180 \text{ rev/min}$ in a plane normal to the horizontal component of Earth's magnetic field $H_{e}$ at a place. If $H_{e} = 0.4 \text{ G}$ at that place,the induced emf between the axle and the rim of the wheel is:

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:

$A$ wire $ab$ of length $l$,mass $m$,and resistance $R$ slides on a smooth,thick pair of metallic rails joined at the bottom as shown in the figure. The plane of the rails makes an angle $\theta$ with the horizontal. $A$ vertical magnetic field $B$ exists in the region. If the wire slides on the rails at a constant speed $v$,then which of the following can be correct for $B$?