Motional EMF

A straight line conductor of length 0.4 m is moved with a speed of $7.0$ ms$^{-1}$ perpendicular to magnetic field of intensity $0.8$ Wb m$^{-2}$. The induced e.m.f. across the conductor is

A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is $2\text{ cm s}^{-1}$, in a direction normal to the shorter side of the loop, will be:

An aeroplane having a wing span of 30 m flies due north with the speed of 170 m/s. Magnetic field $B = 3.6 \times 10^{-5}$ T. The potential difference between the tips of the wings will be

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $\left(g = 10\text{ m/s}^{2}\right)$ through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travels a vertical distance of 200 m is ______ mV.

A long metal rod of length 'L' completes the circuit. The area of the coil is perpendicular to magnetic field 'B'. Total resistance of the circuit is 'R'. The force needed to move the rod in the direction as shown with constant speed 'V' is

A metal rod of length 'L' completes the circuit as shown. The area of the circuit is perpendicular to magnetic field 'B'. Total resistance of the circuit is 'R'. The force needed to move the rod in the direction as shown with constant speed 'V' is

A square loop of area $25$ cm$^{2}$ has a resistance of $10\ \Omega$. The loop is placed in uniform magnetic field of magnitude $40$ T. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in one second will be

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is $2\ \Omega$ then the force needed to move the rod towards right with constant speed $(v)$ of $1.5\text{ m/s}$ is ______ N.

A long rectangular conducting loop of width '$l$' mass '$m$' and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ($g$ = acceleration due to gravity)

$XPQY$ is a vertical smooth long loop having a total resistance $R$ where $PX$ is parallel to $QY$ and separation between them is $l$. A constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. A rod $CD$ of length $L(L > l)$ and mass $m$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is $\underline{\qquad}\ \text{m/s. }(g =$ acceleration due to gravity)

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^\circ$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ______ mV. (Take $g = 10\text{ m/s}^2$)

Initially a rectangular coil with length vertical is moving out with constant velocity ' $v$ ' in a constant magnetic field ' $B$ ' towards right. Now the same coil is rotated through $90^\circ$ in same plane in same magnetic field B and the coil is moving with same velocity $\mathbf{v}$. The magnitude of induced e.m.f. is now

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf $(\varepsilon)$ with time $(t)$ is given by

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of $10\text{ cm/s}$, induced emf between points A and E is ________ mV.

A simple pendulum with bob of mass m and conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of earth's magnetic field in the direction perpendicular to swing is B. Maximum e.m.f. induced across the pendulum is ( $g =$ acceleration due to gravity)

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E ∝ tn, then value of n is _________.

A long rectangular conducting loop of width ' $l$ ', mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' B '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velocity ' $V$ ' is

A horizontal straight wire $5\text{ m}$ long extending from east to west is falling freely at right angle to horizontal component of earths magnetic field $0.60 \times 10^{-4}\text{ Wb m}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is $10\text{ ms}^{-1}$ is _________ $\times 10^{-3}\text{ V}$.

A square loop of side $15\text{ cm}$ is being moved towards right at a constant speed of $2\text{ cm/s}$ as shown in figure. The front edge enters the $50\text{ cm}$ wide magnetic field at $t = 0$. The value of induced emf in the loop at $t = 10\text{ s}$ will be:

A square loop ABCD is moving with constant velocity ' $\vec{v}$ ' in a uniform magnetic field ' $\vec{B}$ ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' $R$ ', then the rate of production of heat energy in the loop is [ L - length of side of loop]

A square loop of area $25\text{ cm}^{2}$ has a resistance of $10\ \Omega$. The loop is placed in uniform magnetic field of magnitude 40 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be

A rectangular loop of sides $12\text{ cm}$ and $5\text{ cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively, moves with a velocity of $5\text{ cm/s}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of $10^{-3}\text{ T/cm}$ along the negative $x$ direction and it is decreasing with time at the rate of $10^{-3}\text{ T/s}$. If the resistance of the loop is $6\text{ m}\Omega$, the power dissipated by the loop as heat is __________ $\times 10^{-9}\text{ W}$.

A conductor $10\text{ cm}$ long is moves with a speed $1\text{ m/s}$ perpendicular to a field of strength $1000\text{ A/m}$. The emf induced in the conductor is (Given: $\mu_0 = 4\pi \times 10^{-7}\text{ Wb/Am}$)

An emf of $0.08\text{ V}$ is induced in a metal rod of length $10\text{ cm}$ held normal to a uniform magnetic field of $0.4\text{ T}$, when moves with a velocity of:

A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be __________.

An air craft of wing span $40\text{ m}$ flies horizontally in earth's magnetic field $5 \times 10^{-5}\text{ T}$ at a speed of $500\text{ m/s}$. The e.m.f. generated between the tips of the wings of the air craft is

If current '$I$' is flowing in the closed circuit with collective resistance '$R$', the rate of production of heat energy in the loop as we pull it along with a constant speed '$V$' is ( $L =$ length of conductor, $B =$ magnetic field)

A metallic cube of side $15\text{ cm}$ moving along $y$-axis at a uniform velocity of $2\text{ ms}^{-1}$. In a region of uniform magnetic field of magnitude $0.5\text{ T}$ directed along $z$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

A conducting wire of length $2500\text{ m}$ is kept in east-west direction, at a height of $10\text{ m}$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $= 25\sqrt{2}\ \Omega$, acceleration due to gravity $g = 10\text{ m/s}^{2},\ B_H = 2 \times 10^{-5}\text{ T}$)

A square loop of area $25\text{ cm}^{2}$ has a resistance of $10\ \Omega$. This loop is placed in a uniform magnetic field of magnitude $40\text{ T}$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in one second, will be

A square loop of area 25 cm$^{2}$ has a resistance of 10 $\Omega$. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1.0 sec, will be

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5$\Omega$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____________ 10$-3$ N.

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

A straight conductor of length 0.6 M is moved with a speed of 10 ms$^{-1}$ perpendicular to magnetic field of induction 1.2 weber m $^{-2}$. The induced e.m.f. across the conductor is

A rectangular loop $PQMN$ with movable arm $PQ$ of length $12\text{ cm}$ and resistance $2\ \Omega$ is placed in a uniform magnetic field of $0.1\text{ T}$ acting perpendicular to the plane of the loop as shown in figure. The resistances of the arms MN, NP and MQ are negligible. The current induced in the loop when arm PQ is moved with velocity $20\text{ ms}^{-1}$ is

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

A wire of length '$L$'; having resistance '$R$' falls from a height '$\ell$' in earth's horizontal magnetic field '$B$'. The current through the wire is ( $g =$ acceleration due to gravity)

A metal wire of length $2500\text{ m}$ is kept in east-west direction, at a height of $10\text{ m}$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $= 25\sqrt{2}\ \Omega,\ g = 10\text{ m/s}^{2}$ and Earth's horizontal component of magnetic field $B_H = 2 \times 10^{-5}\text{ T})$

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 $\times$ 10$-$4 Wb/m2 and the angle of dip is 60$^{\circ}$. The emf induced between the tips of the plane wings will be __________.

A wire of length 1 m is moving at a speed of 2 m/s perpendicular homogenous magnetic field of 0.5 T. The ends of the wire are joined to resistance 6$\Omega$. The rate at which work is being done to keep the wire moving at that speed is

The magnetic field in a region is given by $\vec{B} = B_o\left(\frac{x}{a}\right)\hat{k}$. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity$\vec{v}$= v0$\hat{i}$. The emf induced in the loop is:

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

Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ 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 I1 and I2 flowing through R1 and R2 respectively is:

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance.

A square loop of side 20 cm and resistance 1$\Omega$ is moved towards right with a constant speed v0. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4$\Omega$. What should be the value of v0 so that a steady current of 2 mA flows in the loop?

An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $l$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is:

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

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms–1, at right angles to the horizontal component of the earth's magnetic field of 0.3 $\times$ 10–4 Wb/m2. The value of the induced emf in wire is:

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

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $\theta$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is:

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ‘v’ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $\sigma$1 and $\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 ms−1. The earth’s magnetic field over Delhi is 5 $\times$ 10−5 T with the declination angle ~ 0° and dip of $\theta$ such that sin $\theta$ = 2/3. If the voltage developed is VB between the lower and upper side of the plane and VW between the tips of the wings then VB and VW are close to:

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure.

The potential difference developed across the ring when its speed is $v$, is

A square frame of side 10 cm and a long straight wire carrying current 1 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 ms${}^{-1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is:

A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5}\text{ N A}^{-1}\text{ m}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2\text{ m}$ long. If the speed of the boat is $1.50\text{ ms}^{-1},$ the magnitude of the induced $\text{emf}$ in the wire of aerial is:

A rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R\,\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are

A rectangular, a square, a circular and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity. $\vec{V} = v\hat{i}$. The magnetic field is directed along the negative z axis direction. The induced emf, during the passes of these loops, out of the field region, will not remain constant for

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 $\text{emf}$ induced in the circuit in terms of $B, l$ and $v$ where $l$ is the width of each tube, will be

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A magnetic induction $B$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced $\text{emf}$ is

A straight line conductor of length $0.4\text{ m}$ is moved with a speed of $7\text{ m/s}$ perpendicular to a magnetic field of intensity $0.9\text{ Wb/m}^{2}$. The induced e.m.f. across the conductor is