$A$ copper disc of radius $0.1 \ m$ is rotated about its centre with $10$ revolutions per second in a uniform magnetic field of $0.1 \ T$ with its plane perpendicular to the field. The e.m.f. induced across the radius of the disc is:

  • A
    $\frac{\pi}{10} \ V$
  • B
    $\frac{2\pi}{10} \ V$
  • C
    $\pi \times 10^{-2} \ V$
  • D
    $2\pi \times 10^{-2} \ V$

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The loop shown moves with a velocity $v$ in a uniform magnetic field of magnitude $B$,directed into the paper. The potential difference between $P$ and $Q$ is $e$. Then:

$A$ ceiling fan having $3$ blades of length $80 \ cm$ each is rotating with an angular velocity of $1200 \ rpm$. The magnetic field of Earth in that region is $0.5 \ G$ and the angle of dip is $30^{\circ}$. The $EMF$ induced across the blades is $N \pi \times 10^{-5} \ V$. The value of $N$ is:

$A$ player with a $3 \text{ m}$ long iron rod runs towards the east with a speed of $30 \text{ km/hr}$. The horizontal component of the Earth's magnetic field is $4 \times 10^{-5} \text{ Wb/m}^2$. If the player is running with the rod in horizontal and vertical positions,then the potential difference induced between the two ends of the rod in the two cases will be:

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