$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $AO = l$ and $OC = 3l$. Then which of the following is incorrect?

$A$ 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 $mV$.

$A$ wire of mass $m$ and length $l$ can slide freely on a pair of smooth,vertical rails (figure). $A$ magnetic field $B$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance $C$. The acceleration of the wire,neglecting any electric resistance,is:

$A$ rectangular loop of length $l$ and breadth $b$ is placed at a distance of $x$ from an infinitely long wire carrying current $i$ such that the direction of the current is parallel to the breadth of the loop. If the loop moves away from the current-carrying wire in a direction perpendicular to it with a velocity $v$,the magnitude of the induced emf in the loop is: ($\mu_0=$ permeability of free space)

$A$ coil of area $10 \ m^2$ is placed in a uniform magnetic field of $0.3 \ Wb \cdot m^{-2}$,with its plane perpendicular to the field. The coil rotates at a uniform rate to complete one revolution in $8 \ s$. Find the average emf (in $V$) in the coil during intervals when the coil rotates from:
$i. 0^{\circ}$ to $90^{\circ}$ position
$ii. 90^{\circ}$ to $180^{\circ}$ position
$iii. 180^{\circ}$ to $270^{\circ}$ position
$iv. 270^{\circ}$ to $360^{\circ}$ position

$A$ pair of parallel conducting rails lie at a right angle to a uniform magnetic field of $2.0\, T$ as shown in the figure. Two resistors,$10\,\Omega$ and $5\,\Omega$,slide without friction along the rails. The distance between the conducting rails is $0.1\, m$. Then: