Motional Electromotive Force

The figure given below shows an arrangement by which current flows through the bulb (X) connected with coil B, when a.c. is passed through coil A.


(i) Name the phenomenon involved.

(ii) If a copper sheet is inserted in the gap between the coils, explain how the brightness of the bulb would change.

A rod of length $5 \mathrm{cm}$ is fixed at one end and it is rotating with an angular speed of $5 \mathrm{rad}/\mathrm{s}$. There is a magnetic field of $2 \mathrm{T}$ along the axis of rotation of the field. Find the EMF induced in the rod in millivolts.

A semicircular insulated conductor of radius $0.5$ $\mathrm{m}$ (lying in $X-Z$ plane) is rotated at uniform angular speed of $4$$\mathrm{rad}{\mathrm{s}}^{-1}$ about an axis passing through one of the ends of the conductor (say $A$) in the presence of an external uniform magnetic field $B_0$. Both the axis of rotation and the magnetic field are normal to the plane of the semicircle. If the induced voltage between the ends of the conductor is $10$ $\mathrm{mV}$. What is the strength of magnetic field in $\mathrm{mT}$ ?

Two parallel rails of a railways track, insulated from each other and with the ground, are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of $72 \mathrm{km}$ ${\mathrm{h}}^{-1}$ along the track. The reading of the millivotmeter (in $\mathrm{mV}$) is (Vertical component of the earth's magnetic induction is$2\times {10}^{-5}\mathrm{T})$,

A copper rod of length $l$ is rotated about one end, perpendicular to the magnetic field $B$, with constant angular velocity $\mathrm{\omega }$. The induced emf between the two ends of the rod is,

A solid metal cube of edge length $2\mathrm{ }\mathrm{cm}$ is moving in a positive $y$ -direction at a constant speed of $6\mathrm{ }\mathrm{m}/\mathrm{s}$. There is a uniform magnetic field of $0.1\mathrm{ }\mathrm{T}$ in the positive $z$ -direction. The potential difference between the two faces of the cube perpendicular to the $x$ -axis, is:

The total charge, induced in a conducting loop, when it is moved in a magnetic field depends on

If a coil of $40$ turns and area $4.0 \mathrm{c}{\mathrm{m}}^2$ is suddenly removed from a magnetic field, it is observed that a charge of $2.0\times {10}^{-\mathrm{4 }}\mathrm{C}$ flows into the coil. If the resistance of the coil is $80 \mathrm{\Omega }$, the magnetic flux density in ${\mathrm{W}\mathrm{b }\mathrm{m}}^{-2}$ is.......

A wheel with 10 $\mathrm{N}$ spokes each of length $L$ is rotated with a uniform angular velocity $\omega$ in a plane normal to the magnetic field $B$. The emf induced between the axle and the rim of the wheel is

In the figure shown, $R$ is a fixed conducting fixed ring of negligible resistance and radius $a$. $PQ$ is

a uniform rod of resistance $r$. It is hinged at the centre of the ring and rotated about this point in clockwise direction with a uniform angular velocity $\omega .$ There is a uniform magnetic field of strength $B$ pointing inwards $r$ is a stationary resistance, then-

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

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

A $2 \mathrm{m}$ long wire is moving with a velocity $1 \mathrm{m} {\mathrm{s}}^{-1}$ in a magnetic field of intensity $0.5 \mathrm{W}\mathrm{b} {\mathrm{m}}^{-2}$ in a direction perpendicular to the field. The emf induced in it will be,

One conducting U-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $v$, then the emf induced in the circuit in terms of $B, l \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }v,\mathrm{ }\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{ }l$ is the width of each tube, will be

When a rod of length $l$ is rotated with angular velocity of $\omega$ in a perpendicular field of induction $B$, about one end, the emf induced across its ends is

A metal rod of resistance $20 \mathrm{\Omega }$ is fixed along a diameter of a conducting ring of radius $0.1 \mathrm{m}$ and lies in the $x-y$ plane. There is a magnetic field $\overrightarrow{\text{B}}=\left(50T\right) \hat{\text{k}}$. The ring rotates with an angular velocity of $\omega =20 \mathrm{rad} {\mathrm{s}}^{-1}$ about its axis. An external resistance of $10 \mathrm{\Omega }$ is connected across the centre of the ring and rim. The current through external resistance is,

A rod of length $10 \mathrm{cm}$, is made up of a conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with a constant angular velocity of $10 \mathrm{rad} {\mathrm{s}}^{-1}$ about point $O$, in a constant magnetic field of $2 \mathrm{T}$, as shown in the diagram. The induced emf between the points $A$ and $B$ of rod will be
             

Find the emf induced between the ends of a semicircular arc. Semicircular arc is rotating about an axis passing through point $A$ and perpendicular to its plane with uniform angular speed $\omega$ in a uniform magnetic field $B$.


                          

A conducting ring of radius r with a conducting spoke is in pure rolling on a horizontal surface in a region having a uniform magnetic field B as shown, v being the velocity of the centre of the ring. Then the potential difference V₀ - V_A is

       

A copper disc of radius 10 cm placed with its plane normal to a uniform magnetic field completes 1,200 rotations per minute. If induced e.m.f. between the centre and edge of the disc is 6.284 mV,   the magnetic induction is (Take $\pi =3\text{.}142\text{)}$