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?

A coil of 250 turns and area 0.1 $m^2$ rotates at 5 rad/s in a uniform magnetic field of $4 imes 10^{-3}$ T. The maximum induced emf is 0.5 V. What is the resistance of the coil if the maximum induced current is 0.1 A?

A wire of length $1\,\,m$ is moving at a speed of $2\,\,m{s^{ - 1}}$ perpendicular to its length and in a homogenous magnetic field of $0.5\,\,T$. The ends of the wire are joined to a circuit of resistance $6\,\,{\rm{\Omega }}$. The rate at which work is being done to keep the wire moving at constant speed is

A square aluminum plate is held stationary above a strong bar magnet. Under what condition would a force be required to maintain its position?

Two identical conducting rods $AB$ and $CD$ are connected to a conducting circular ring as shown. The entire system is placed in a uniform magnetic field $B$ directed perpendicular to the plane of the ring. If the rod $AB$ rotates with a constant angular velocity $\omega$ and $CD$ rotates with $2\omega$, the emf induced between the points $A$ and $D$ is:

The self induced emf in a coils of ${\rm{0}}.{\rm{4}}\,\,{\rm{henry}}$ self inductance when current in it is changing at the rate of ${\rm{50}}\,\,{\rm{A}}{{\rm{s}}^{{\rm{ - 1}}}}$, is

A metal disc of radius $r$ rotates with an angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to its plane. The emf induced between the center and the rim of the disc is:

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 copper rod of length $l$ is rotated about one end perpendicular to a uniform magnetic field $B$ with constant angular velocity $\omega$. The induced emf between the ends of the rod is $\epsilon$. If the length of the rod is doubled and the angular velocity is halved, the new induced emf will be:

A conducting rod of length $l$ moves with a constant velocity $v$ in a uniform magnetic field $B$. The field is perpendicular to the rod and the velocity. The rod slides on conducting rails forming a closed circuit with resistance $R$. If the force required to keep the rod moving with constant velocity is $F$, which expression correctly relates $F$, $B$, $l$, $v$, and $R$?