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 conducting circular loop is placed in a uniform magnetic field of induction $B$ tesla with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate $\left( {\frac{{dr}}{{dt}}} \right)$. Then, the induced emf at the instant when the radius is $r$,is

For a coil having L = 2 mH, current flows at the rate of ${10^3}\;{\rm{A}}{{\rm{s}}^{ - 1}}$. The emf induced is

A metal conductor of length ${\rm{1 m}}$ rotates vertically about one of its ends at angular velocity $5\,\,rad\,\,{{\rm{s}}^{ - 1}}$. If the horizontal component of earth’s magnetic field is $0.2\,\, imes {10^{ - 4}}\,{\rm{T}}$, then the emf developed between the two ends of the conductor is

A $10\,\,metre$ wire kept in east-west direction is falling with velocity $5\,\,m/\sec$ perpendicular to the field $0.3\,\, imes \,{10^{ - 4}}\,\,Wb/{m^2}$. The induced e.m.f. across the terminal 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 horizontal straight wire ${\rm{20}}\,{\rm{ m}}$ long extending from east to west is falling with a speed of ${\rm{5}}{\rm{.0}}\,\,{\rm{m}}{{\rm{s}}^{ - 1}}$,at right angles to the horizontal component of the earth’s magnetic field $0.030\,\, imes \,\,{10^{ - 4}}\,\,{\rm{Wb}}{{\rm{m}}^{ - 2}}{\rm{.}}\,{\rm{}}$ the instantaneous value of the emf induced in the wire will be

A conducting square loop of side $l$ and resistance $R$ is moving with a constant velocity $v$ perpendicular to one of its sides and entering a uniform magnetic field $B$ perpendicular to the plane of the loop. What is the magnitude of the induced current in the loop as a function of time $t$, where $t=0$ is the instant when the loop starts entering the field?

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 straight conductor of length $4\,\,m$ moves at a speed of $10\,\,m/s$. When the conductor makes an angle of ${30^0}$ with the direction of magnetic field of induction of $0.1\,\,wb.{m^2}$ then induced emf is

The magnetic field in a coil of ${\rm{100}}$ turns and $40{\mkern 1mu} {\mkern 1mu} \,square\,\,cm$ area is increased from $1\,\,tesla$ to $6\,\,tesla$ in $2\,\,seconds$. The magnetic field is perpendicular to the coil. The e.m.f. generated in it is