Motional Electromotive Force

A wire of length $1 \mathrm{m}$ moving with velocity $8 \mathrm{m} {\mathrm{s}}^{-1}$ at right angles to a magnetic field of $2 \mathrm{T}$. The magnitude of induced emf, between the ends of wire will be ___________.

A metallic rod of length $L$ is rotated with an angular speed of $\omega$ normal to a uniform magnetic field $B$ about an axis passing through one end of rod as shown in figure. The induced emf will be :

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A metallic rod of length $20 \mathrm{cm}$ is placed in North-South direction and is moved at a constant speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ towards East. The horizontal component of the Earth's magnetic field at that place is $4\times {10}^{-3} \mathrm{T}$ and the angle of dip is $45°$. The emf induced in the rod is _____ $\mathrm{mV}$.

A metallic conductor of length $1 \mathrm{m}$ rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times {10}^{-4} \mathrm{T}$, then emf induced between the two ends of the conductor is

A constant magnetic field of $1 \mathrm{T}$ is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius $1 \mathrm{m}$ is moving with a constant velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$-axis. At $t=0 \mathrm{s}$, the centre $\mathrm{O}$ of the ring is at $\mathrm{x}=-1 \mathrm{m}$. What will be the value of the induced emf in the ring at $\mathrm{t}=1 \mathrm{s}$ ? (Assume the velocity of the ring does not change.)

A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure.

Two resistors $R_1$ and $R_2$ are connected across the ends of the rails. There is a uniform magnetic field $\overrightarrow{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$.

The correct statement about the directions of induced currents $I_1$ and $I_2$ flowing through $R_1$ and $R_2$ respectively is :

An aeroplane, with its wings spread $10 \mathrm{m},$ is flying at a speed of $180 \mathrm{km} {\mathrm{h}}^{-1}$ in a horizontal direction. The total intensity of earth's field at that part is $2.5\times {10}^{-4} \mathrm{Wb} {\mathrm{m}}^{-2}$ and the angle of dip is $60°.$ The EMF induced between the tips of the plane wings will be

The figure shows a square loop $L$ of side $5\mathrm{ }\mathrm{c}\mathrm{m}$ which is connected to a network of resistances. The whole setup is moving towards the right with a constant speed of $1 \mathrm{c}\mathrm{m} {\mathrm{s}}^{-1}$ . At some instant, a part of $L$ is in a uniform magnetic field of $1\mathrm{T}$ perpendicular to the plane of the loop. If the resistance of $L$ is $1.7\mathrm{ }\mathrm{\Omega },$ the current in the loop at that instant will be close to:

A thin strip $10 \mathrm{c}\mathrm{m}$ long is on a $\mathrm{U}$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5 \mathrm{N}\mathrm{ }{\mathrm{m}}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of $0.1 \mathrm{T}.$ If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $\mathrm{e}$ is $\mathrm{N}$ . If the mass of the strip is $50$ grams, its resistance $10\mathrm{\Omega }$ and air drag negligible, $\mathrm{N}$ will be close to:

A $10 \mathrm{m}$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0 \mathrm{m} {\mathrm{s}}^{-1},$ at right angles to the horizontal component of the earth's magnetic field of $0.3\times {10}^{-4} \mathrm{Wb} {\mathrm{m}}^{-2}.$ The value of the induced emf in the wire is:

A solid metal cube of edge length $2\mathrm{ }\mathrm{cm}$ is moving in the positive $\mathrm{y}$-direction, at a constant speed of $6\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. There is a uniform magnetic field of $0.1\mathrm{ }\mathrm{T}$ in the positive $\mathrm{z}$-direction. The potential difference between the two faces of the cube, perpendicular to the $\mathrm{x}$-axis, is

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $\mathrm{v}$ in a uniform magnetic field $\mathrm{B}$ going into the plane of the paper (see figure). If charge densities ${\mathrm{\sigma }}_1$ and ${\mathrm{\sigma }}_2$ are induced on the left and right surfaces respectively of the sheet, then (ignore fringe effects)

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is $240 m{s}^{-1}.$ The earth's magnetic field over Delhi is $5\times {10}^{-5}T$ with the declination angle $~0^o$ and dip of $\theta$ such that $\sin \theta =\frac{2}{3}.$If the voltage developed is $V_B$ between the lower and upper side of the plane and $V_W$ between the tips of the wings then $V_B and V_W$ are close to :

A square frame of side $10 \mathrm{cm}$ and a long straight wire carrying current $1 \mathrm{A}$ are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at $x=10 \mathrm{cm}$ from the wire is

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is: