$A$ 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?

$A$ circular coil of radius $30 \ cm$,having $1$ turn and a resistance of ${\pi ^2} \ \Omega$,is placed in a magnetic field of $10^{-2} \ T$. The coil rotates about its diameter with a speed of $200 \ rpm$ in a direction perpendicular to the magnetic field. The value of the induced $AC$ current in the coil will be . . . . . . $mA$.

$A$ train is moving with a speed of $30 \, m \, s^{-1}$ in the north-south direction on rails separated by $2 \, m$. If the vertical component of the Earth's magnetic field is $8 \times 10^{-5} \, T$,the induced $e.m.f.$ is: (in $, V$)

$A$ square metallic wire loop of side $0.1 \, m$ and resistance $1 \, \Omega$ is moved with a constant velocity in a magnetic field of $2 \, Wb/m^2$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop, and the loop is connected to a network of resistances. What should be the velocity of the loop to have a steady current of $1 \, mA$ in the loop? (in $cm/sec$)

$A$ rod of length $l$ is oscillating as a physical pendulum about one of its ends with a small angular amplitude $\alpha$ in a crossed magnetic field $B$. The maximum $emf$ induced in the rod will be:

$A$ metal rod $AB$ of length $50 \text{ cm}$ is moving at a velocity $8 \text{ ms}^{-1}$ in a magnetic field of $2 \text{ T}$. If the field is at $60^{\circ}$ with the plane of motion as shown in the figure,then the potentials $V_A$ and $V_B$ are related by