A conducting rod of length $l$ rotates with a constant angular velocity $\omega$ about one end in a uniform magnetic field $B$ perpendicular to the plane of rotation. A capacitor $C$ is connected in series with the rod and a resistance $R$. If the steady state charge on the capacitor is $Q$, which of the following expressions is correct?

The number of turns in the coil of an ac generator is ${\rm{5000}}$ and the area of the coil is $0.25\,\,{m^2}$. The coil is rotated at the rate of $100\,\,cycles/\sec$ in a magnetic field of $0.2\,\,W/{m^2}$. The peak value of the emf generated is nearly

At a place the value of horizontal component of the earth’s magnetic field $H$ is $3\,\, imes \,{10^{ - 5}}\,weber/{m^2}$. A metallic rod $AB$ of length $2\,\,m$ placed in east-west direction, having the end $A$ towards east, falls vertically downward with a constant velocity of $50\,\,m/s$. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends

A square loop of side 10 cm is moved with a velocity of 5 m/s perpendicular to a magnetic field of 0.5 T. The emf induced in the loop is:

A helicopter rises vertically with a speed of ${\rm{100 }}\,{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}$. If helicopter has length ${\rm{10}}\,\,{\rm{m}}$ and horizontal component of earth’s magnetic field is $5\,\, imes {10^{ - 3}}\,\,{\rm{Wb}}{{\rm{m}}^{ - 2}}$,then the induced emf between the tip of nose and tail of helicopter is

A rectangular coil of 500 turns and area 20 $m^2$ is rotating about its vertical axis at 5 rad $s^{-1}$ in a uniform horizontal magnetic field of $2 imes 10^{-4} T$. If the electrical resistance of the coil is 5 $\Omega$, then the maximum induced current in the coil will be:

In a dc motor, induced e.m.f. will be maximum

There is an aerial  ${\rm{1 m}}$ long in a car. It is moving from east to west with a velocity of $100\,\,km{{\rm{h}}^{ - 1}}$. If the horizontal component of earth’s magnetic field is ${\rm{0}}{\rm{.18}}$ gauss, this induced emf is nearly

A metal of radius ${\rm{100}}\,\,{\rm{cm}}$ is rotated at a constant angular speed of ${\rm{60}}\,\,{\rm{rad}}{{\rm{s}}^{ - 1}}$ in a plane at right angles to an external field of magnetic induction ${\rm{0}}{\rm{.05}}\,\,{\rm{Wb}}{{\rm{m}}^{ - 2}}$. The emf induced between between the centre and a point on the rim will be

A circular metal plate of radius $R$ is rotating with a uniform angular velocity $\omega$ with its plane perpendicular to a uniform magnetic field $B$. Then the emf developed between the centre and the rim of the plate is

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