Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

$A$ circular coil of area $3 \times 10^{-2} \, m^2$, $900$ turns, and a resistance of $1.8 \, \Omega$ is placed with its plane perpendicular to a uniform magnetic field of $3.5 \times 10^{-5} \, T$. The current induced in the coil when it is rotated through $180^{\circ}$ in half a second is (in $ \, mA$)

An aircraft with a wing-span of $40\, m$ flies with a speed of $1080\, km\, h^{-1}$ in the eastward direction at a constant altitude in the northern hemisphere,where the vertical component of earth's magnetic field is $1.75 \times 10^{-5} \, T$. Then the emf that develops between the tips of the wings is.......$V$

$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$

$A$ thin strip $10\, cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5\, N/m$ (see figure). The assembly is kept in a uniform magnetic field of $0.1\, T$. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$. If the mass of the strip is $50\, g$, its resistance $10\, \Omega$ and air drag is negligible, $N$ will be close to:

$A$ fixed rectangular conductor $ODBAC$ has negligible resistance (where $CO$ is not connected). $A$ conductor $OP$ rotates clockwise with an angular velocity $\omega$ as shown in the figure. The entire system is in a uniform magnetic field $B$ directed along the normal to the surface of the rectangular conductor $ABDC$. The conductor $OP$ is in electric contact with $ABDC$. The rotating conductor has a resistance of $\lambda$ per unit length. Find the current in the rotating conductor as it rotates by $180^{\circ}$.