$A$ 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

$A$ metal rod of length '$L$' completes the circuit as shown. The area of the circuit is perpendicular to the magnetic field '$B$'. The total resistance of the circuit is '$R$'. The force needed to move the rod in the direction as shown with a constant speed '$V$' is

$A$ 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?

$A$ uniform magnetic field of $0.4 \ \text{T}$ acts perpendicular to a circular copper disc $20 \ \text{cm}$ in radius. The disc is rotating with a uniform angular velocity of $10 \pi \ \text{rad s}^{-1}$ about an axis passing through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim (in $\text{V}$)? $(\pi = 3.14)$

$A$ rod of length $l$ is rotating with constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of rotation. The rod is marked at points $0, 1, 2, \dots, 8$ at equal spacing. What is the nature of the potential difference between consecutive points as we move from left to right?

$A$ horizontal straight wire $20 \; m$ long extending from east to west is falling with a speed of $5.0 \; m/s$ at right angles to the horizontal component of the earth's magnetic field $0.30 \times 10^{-4} \; Wb/m^2$. The instantaneous value of the emf induced in the wire will be ......... $mV$.