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 $R$?

A horizontal straight wire ${\rm{10 m}}$ long extending from east to west is falling with a speed of ${\rm{5}}{\rm{.0}}\,\,{\rm{m}}{{\rm{s}}^{{\rm{( - 1)}}}}$, at right angles to the horizontal component of the earth’s magnetic field of strength $0.30 imes {10^{ - 4}}\,\,{\rm{Wb}}{{\rm{m}}^{ - 2}}$. the instantaneous value of the induced potential gradient in the wire, from west to east, is

The expression for magnetic induction inside a solenoid of length L, carrying a current i and having N number of turns is

A copper rod of length $l$ is rotated about one end perpendicular to the magnetic field $B$ with constant angular velocity $\omega$. The induced e.m.f. between the two ends is

The unit of motional emf is:

A conducting rod of length $l$ is moving in a transverse magnetic field of strength $B$ with velocity $v$. The resistance of the rod is $R$. the current in the rod is

The length of a potentiometer wire is 1 m and its resistance is $4\,\Omega$. A current of $5\,mA$ is flowing in it. An unknown source of emf is balanced on $40{\mkern 1mu} \,cm$ length of this wire, then find the emf of the source.

A coil of ${\rm{1000}}$ turns is wound on a book and this book is lying on the table. The vertical component of earth’s magnetic field is $0.6 imes {10^{ - 4}}T$ and the area of the coil is $0.05\,\,{{\rm{m}}^{ 2}}$. The book is turned over once about a horizontal axis is ${\rm{0}}{\rm{.1 s}}$. This average emf induced in the coil is

A uniform circular metal disc of radius ‘R’ is rotating about a vertical axis passing through its center and perpendicular to its plane with constant frequency f. If ${B_H}$ and ${B_V}$ are horizontal and vertical components of the earth’s magnetic field respectively, then the induced emf between its centre and the rim is

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 direction of the induced current in a conductor moving in a magnetic field is given by: